SINGLE CHOICE QUESTIONS
1. A particle is projected from origin O with a velocity (30 i + 40 j) m/s. Then the position vector of the particle 5 seconds later is : (take g = 10 m/s2)
(A) 150 i + 200j m (B) 150 i + 75 j m
(C) 30i + 75j m (D) Nothing can be predicted.
2. For a particle moving in a straight line, the displacement of the particle at time t is given by S = t3
– 6t2 + 3t + 7
What is the velocity of the particle when its acceleration is zero?
(A) – 9 m s–1 (B)
– 12 m s–1 (C) 3 m s–1 (D) 42 m s–1
3. The velocity of a particle moving on the x-axis is given by v = x2 + x where v is in m/s and x is in m. Find its
acceleration in m/s2 when passing through the point x = 2m
(A) 0 (B) 5 (C) 11 (D) 30
4. A parachutist drops freely from an aeroplane for 10 s before the parachute opens out. Then he descends with a net retardation of 2.5 ms–2. If he bails out of the plane at a height of 2495 m and g = 10 ms–2, his velocity on
reaching the ground will be
(A) 2.5 ms–1 (B) 7.5 ms–1 (C) 5 ms–1 (D) 10 ms–1
5. A particle can travel from point A to B from two different paths 1 and 2, as shown, in same interval of time. Then which of the following is incorrect?
(A) Average velocity along the two paths must be equal (B) The particle may travel along both the paths unaccelerated
(C) The direction of instantaneous velocity along the path 1 & 2 can be same for a maximum of two point on the paths.
(D) The average and instantaneous velocity along path 1 can have same direction.
6. Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains when both have stopped, is :
(A) 120 m (B) 280 m (C) 60 m (D) 20 m.
REVISION TEST - 01
Course : VIJAY (R)
TOPIC : KINEMATICS
(1-D & RELATIVE MOTION)
Time : 3 Hrs. Max. Marks : 133
Instructions :
1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 4 marks (no negative marking).
3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each match the column question 6 marks (no negative marking).
5. For each correct assertion/reason question 3 marks (with 1 mark negative marking).
7. Position (Km) - Time (min.) graph is shown for two cars ‘A’ and ‘B’. Both
collide at time t = 150 minute. Then the distance of position ‘R’ of accident
from the starting point ‘Q’ of car A will be. (Initial distance between the two
cars is 500 km) (Position in the graph shows the distance of the two cars from the point ‘Q’) -
(A) 200 km (B) 300 km (C) 250 km (D) 400 km
8. A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is
(A) n ) 1 n ( v (B) n ) 1 n ( v 2 (C) n ) 1 n ( v 2 (D) n ) 1 n ( v
9. A boat is rowed across a river at the rate of 4.5 km/hr. The river flows at the rate of 6 km/hr. The velocity of boat in m/s is:
(A) 3.1 (B) 2.1 (C) 2.9 (D) 5
10. An aeroplane is to go along straight line from A to B, and back again. The relative speed with respect to wind is V.. The wind blows perpendicular to line AB with speed . The distance between A and B is l. The total time for the round trip is:
(A) 2 2 V
v
2 (B) 2 2 Vv
v
2 (C) 2 2 Vv
V 2 (D) 2 2 V v
211. A man can swim in still water with a speed of 3 m/s. x and y axis are drawn along and normal to the bank of river flowing to right with a speed of 1 m/s. The man starts swimming from origin O at t = 0 second. Assume size of man to be negligible. Find the equation of locus of all the possible points where man can reach at t = 1 sec.
Vriver=1m/s flow y O river x (A) (x – 1)2 + y2 = 3 (B) (x – 1)2 + y2 = 9 (C) x2 + (y – 1)2 = 3 (D) x2 + (y – 1)2 = 9
12. P is a point moving with constant speed 10 m/s such that its velocity vector always maintains an angle 60° with line OP as shown in figure (O is
a fixed point in space). The initial distance between O and P is 100 m. After what time shall P reach O.
(A) 10 sec. (B) 15 sec. (C) 20 sec. (D) 20 3 sec
13. During a rainy day, rain is falling vertically with a velocity 2m/s. A boy at rest starts his motion with a constant acceleration of 2m/s2 along a straight road. Find the rate at which the angle of the axis of umbrella with vertical should be changed so that the rain always falls parallel to the axis of the umbrella.
(A) 2 t 1 1 (B) 2 t 1 2 (C) 2 t 2 1 (D) 2 t 2 1 1
14. A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instant train starts to move with constant acceleration . The path of the particle as seen by the person who drops the stone is :
(A) parabola
(B) straight line for sometime & parabola for the remaining time (C) straight line
(D) variable path that cannot be defined
15. Two boats A and B having same speed relative to river are moving in a river. Boat A moves normal to the river current as observed by an observer moving with velocity of river current. Boat B moves normal to the river as observed by the observer on the ground.
(A) To a ground observer boat B moves faster than A (B) To a ground observer boat A moves faster than B
(C) To the given moving observer boat B moves faster than A (D) To the given moving observer boat A moves faster than B
16. For four particles A, B, C & D, the velocities of one with respect to other are given as VDC is 20 m/s towards
north, VBC is 20 m/s towards east and VBA is 20 m/s towards south. Then VDA is
(A) 20 m/s towards north (B) 20 m/s towards south (C) 20 m/s towards east (D) 20 m/s towards west
MULTIPLE CHOICE QUESTIONS
17. A particle moves in xy plane in such a way that its distance ‘r’ from the origin depends upon time ‘t’ as r = 3t.
The angle ‘’ made by its position vector with the positive x-axis at any time ‘t’ is given as ; = 2t. Here r is
in metres, in rad and t in seconds.
(A) The particle moves in circular motion. (B) At time t = 0.5 s, its speed is 3 2 m/s.
(C) At time t = 0.5 s, its velocity vector makes an angle 45° with its position vector at the same time.
(D) At time t = 0.5 s, its velocity vector makes an angle 30° with its position vector at the same time.
18. Two particles, one with constant velocity 50m/s and the other with uniform acceleration 10m/s2, start moving simultaneously from the same position in the same direction. They will be at a distance of 125m from each other after
(A) 5 sec. (B) 5(1 +
2) sec. (C) 10sec. (D) 10(
2 + 1)sec.19. A man standing on the edge of the terrace of a high rise building throws a stone vertically up with a speed of 20 m/s. Two seconds later an identical stone is thrown vertically downwards with the same speed of 20 m/s. Then:
(A) the relative velocity between the two stones remain constant till one hits the ground (B) both will have the same kinetic energy when they hit the ground
(C) the time interval between their hitting the ground is 2 seconds
(D) if the collisions on the ground are perfectly elastic both will rise to the same height above the ground.
20. A cart with a mass M = 1/2 kg is connected by a string to a weight of mass m = 200 g. At the initial moment the cart moves to the left along a horizontal plane at a speed V0 = 7 ms 1. All the surfaces are smooth
(g = 9.8 ms 2)
(A) the distance covered by cart in 5 s is zero
(B) after 5 s weight of mass m will be in same position (C) the distance covered by cart in 5 s is 17.5 m (D) none of the above
21. A particle moves with an initial velocity v0 and retardation v, where v is its velocity at any time t ( is
a positive constant).
(A) the particle will cover a total distance of v0/
(B) the particle will continue to move for a very long time (C) the particle will stop shortly
(D) the velocity of particle will become v0/2 after time 1/.
22. A particle is moving rectilinearly so that its acceleration is given as a = 3t2+1 m/s2.Its initial velocity is zero. (A) The velocity of the particle at t=1 sec will be 2m/s.
(B) The displacement of the particle in 1 sec will be 2m. (C) The particle will continue to move in positive direction.
(D) The particle will come back to its starting point after some time.
23. A man is standing on a road and observes that rain is falling at angle 45º with the vertical. The man
starts running on the road with constant acceleration 0.5 m/s2. After a certain time from the start of the motion, it appears to him that rain is still falling at angle 45º with the vertical, with speed 2 2 m/s .
Motion of the man is in the same vertical plane in which the rain is falling. Then which of the following statement(s) are true.
(A) It is not possible
(B) Speed of the rain relative to the ground is 2 m/s.
(C) Speed of the man when he finds rain to be falling at angle 45º with the vertical, is 4m/s.
COMPREHENSION
Comprehension - 1Raindrops are falling with a velocity 10 2 m/s making an angle of 450 with the vertical. The drops appear to be falling vertically to a man running with constant velocity. The velocity of rain drops change such that the rain drops now appear to be falling vertically with 3 times the velocity it appeared earlier to the same person running with same velocity.
24. The magnitude of velocity of man with respect to ground is
(A) 10 2 m/s (B) 10 3 m/s (C) 20 m/s (D) 10 m/s
25. After the velocity of rain drops change, the magnitude of velocity of raindrops with respect to ground is (A) 20 m/s (B) 20 3 m/s (C) 10 m/s (D) 10 3 m/s
26. The angle (in degrees) between the initial and the final velocity vectors of the raindrops with respect to the ground is
(A) 8 (B) 15 (C) 22.5 (D) 37
Comprehension - 2
A overhead bridge, a subway and a road start from A and again meet at B. The minimum distance between A and B, which is same as the length of the road AB, is 2 km. The overbridge and the subway form a semicircular arc above and below the road. A laser sensor is fixed (embedded) in the road. An Autorickshaw takes the overbridge from A and a taxi takes the subways from B.The laser sensor gives a beep when the linear distances between point A and the autorickshaw is same as that between the rickshaw and the laser sensor which also equals the distance of laser source from point A.
27. If the time t, for the laser starts when the autorickshaw just enters the bridge from point A and at t = 240 sec, laser the gives a beep, what is the speed of the autorickshaw ?
(A) 4.36 m/s (B) 1.21 m/s (C) 8.16 m/s (D) 16.32 m/s
28. The autorickshaw takes the overhead bridge from A and on reaching B, immediately takes the subway to come back to A, while the taxi starts from B travels to and fro from B to A continuously by road. If the auto and the taxi travel with constant speeds of
2
km/hr and 3 km/hr respectively, how frequently do they meet at A ?
(A) every 4 hours (B) every 3 n 2 hours, n = 3,6,9,.... (C) every 3 2
hours (D) they never meet
29. Due to heavy rains, the flyover and the roads were blocked and all the vehicles had to take the subway. The autorickshaw and the taxi started from A and B respectively with the speeds
2 and 3 2 km/hr respectively. After how much time did they meet ?
(A) 6 7 hours (B) 7 6 hours (C) 3 2 hours (D) 7 6 hours
Comprehension - 3
Mr. Shyam drives his car at uniform speed from bottom of a mountain to the top in 20 minutes along a helical path as shown. At the beginning the speedometer of his car shows 8315 km, while on reaching the top it reads 8335 km.(Take upward as positive y-axis and positive x-y-axis towards right)
30. The total distance covered is :
(A) 10 km (B) 20 km (C) 25 km (D) can not be determine
31. His displacement vector during the journey is :
(A) (3ˆi4ˆj)km (B) 3 km (C) 5 km (D) none of these
32. The average velocity during the journey is :
(A) (9ˆi12ˆj) km/hr (B) (2.5ˆi3.3ˆj) m/s (C) (25/8) m/s (D) None of these
MATCH THE COLUMN
33. Two particles A and B moving in x-y plane are at origin at t = 0 sec. The initial velocity vectors of A and B are uA= 8 iˆ m/s and uB
= 8 jˆ m/s. The acceleration of A and B are constant and are aA= –2ˆi m/s2
and aB= – 2ˆj m/s2. Column gives certain statements regarding particle A and B. Column gives
corresponding results. Match the statements in column with corresponding results in Column .
Column I Column II
(A) The time (in seconds) at which velocity (p) 16 2
of A relative to B is zero
(B) The distance (in metres) between A and B (q) 8 2
when their relative velocity is zero.
(C) The time (in seconds) after t = 0 sec, (r) 8 at which A and B are at same position
(D) The magnitude of relative velocity of A and B (s) 4 at the instant they are at same position.
34. A particle is moving along a straight line. Its velocity varies with time as v = kt, where k is a positive constant and t is the time. Match the graphs in Column with the statements in Column
Column Column
(A) Acceleration versus time curve (p)
(B) Acceleration versus displacement curve (q)
(C) Velocity versus time curve (r)
ASSERTION / REASON
35. Assertion : If acceleration of a particle is decreasing then it is possible that velocity is increasing with time. Reason : Acceleration is rate of change of velocity.
(A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false.
(D) if Assertion is false, but the Reason is true.
36 STATEMENT–1 : The equation of distance travelled by a particle moving in a straight line with constant
acceleration in nth second is S
n = u + (2n – 1)2 a
, where letters have usual meaning, is dimensionally incorrect.
STATEMENT–2: For every equation relating physical quantities to be true, it must have dimensional
homogenity.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
37. STATEMENT-1 : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously
from same point on one bank may reach opposite bank simultaneously moving along different paths.
STATEMENT-2 : For boats to cross the river in same time. The component of their velocity relative to river in
direction normal to flow should be same.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Answer Key (Revision Test - 01)
1. (B) 2. (A) 3. (D) 4. (C) 5. (B)
6. (D) 7. (B) 8. (C) 9. (B) 10. (A)
11. (B) 12. (C) 13. (A) 14. (C) 15. (B)
16. (D) 17. (B)(C) 18. (A)(B) 19. (A)(B)(C)(D) 20. (B) (C) 21. (A)(B) 22. (A)(C) 23. (C)(D) 24. (D) 25. (A)
26. (B) 27. (A) 28. (D) 29. (B) 30. (B)
31. (A) 32. (A) 33. (A) s (B) p (C) r (D) q
34. (A) p (B) p (C) q (D) r 35. (A) 36 (D) 37. (A)
SINGLE CHOICE QUESTIONS
REVISION TEST - 02
COURSE : VIJAY (R)
TOPIC : PROJECTILE MOTION
SUBJECT : PHYSICS
Time : 1½ Hrs. Max. Marks : 48
Instructions :
1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each match the column question 6 marks (no negative marking).
4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).
1. A particle when projected in vertical plane moves along the fixed smooth surface with initial velocity 20 m/s at an angle of 60º, so that its normal reaction on the
surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection A will be: (A) 30º (B) 45º (C) tan1 2 (D) tan1 2
2. A particle moves along the parabolic path y = ax2 in such a way that the y-component of the velocity remains constant, say c. The x and y coordinates are in meters. Then acceleration of the particle at x =1 m is (A) ac
k
ˆ
(B) 2ac2jˆ
(C) iˆ a 4 c 2 2 (D) iˆ a 2 c 3. An object is thrown from a point ‘A’ horizontally from a tower and hits the
ground 3s later at B. The line from ‘A’ to ‘B’ makes an angle of 30º with the
horizontal. The initial velocity of the object is : (take g = 10 m/s2)
(A) 15 3 m/s (B) 15 m/s (C) 10 3 m/s (D) 25/ 3 m/s
4. A particle is projected from a point P (2, 0, 0)m with a velocity 10 m/s making an angle 45º with the
horizontal. The plane of projectile motion passes through a horizontal line PQ which makes an angle of 37º with positive x-axis, xy plane is horizontal. The coordinates of the point where the particle will
strike the line PQ is: (Take g = 10 m/s2)
(A) (10, 6, 0)m (B) (8, 6, 0)m (C) (10, 8, 0)m (D) (6, 10, 0)m
5. A car starts with constant acceleration a = 2m/s2 at t = 0. Two coins are released from the car at t = 3 & t = 4. Each coin takes 1 second to fall on ground. Then the distance between the two coins will be (Assume coin sticks to the ground)
(A) 9 m (B) 7 m (C) 15 m (D) 2m
6. Velocity of a stone projected, 2 second before it reaches the maximum height, makes angle 53° with the
horizontal then the velocity at highest point will be
(A) 20 m/s (B) 15 m/s (C) 25 m/s (D) 80/3 m/s
7. Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from G1 is u1 and that from G2 is u2. The guns aim exactly towards each other The ratio u1 : u2 such that the shells collide with each other in air is (Assume that there is no resistance of air)
(A) 1 : 2 (B) 1 : 4
(C) will not collide for any ratio (D) will collide for any ratio
8. A stone is projected from level ground such that its horizontal and vertical components of initial velocity are ux = 10 m/s and uy = 20 m/s respectively. Then the angle between velocity vector of stone one second before and one second after it attains maximum height is :
(A) 30° (B) 45° (C) 60° (D) 90°
COMPR EHENSI ON
ComprehensionA stone is projected from level ground with speed u and at an angle with horizontal. Some how the
acceleration due to gravity (g) becomes double (that is 2g) immediately after the stone reaches the maximum height and remains same thereafter. Assume direction of acceleration due to gravity always vertically downwards.
9. The total time of flight of particle is : (A) 23using (B) using
2 1 1 (C) g sin u 2 (D) 2 1 2 g sin u
10. The horizontal range of particle is (A) g 2 sin u 4 3 2 (B) 2 1 1 g 2 2 sin u2 (C) g u2 sin2 (D) 2 1 2 g 2 2 sin u2
11. The angle which the velocity vector of stone makes with horizontal just before hitting the ground is
given by :
(A) tan = 2 tan (B) tan = 2 cot (C) tan = 2 tan (D) tan = 2 cot
MATCH THE COLUMN
12. Match the following.The projectile collides perpendicularly with the inclined plane. (Refer the figure)
u
(a) Maximum height attained by the (P) zero projectile from the ground
(b) Maximum height attained by (Q) g the projectile from Inclined plane
(c) Acceleration of the projectile before (R)
cos g 2 sin u2 2 striking the inclined plane
(d) Horizontal component of acceleration of the projectile. (S)
g 2 ) ( sin u2 2
13. Assertion : For a projectile up the incline maximum angle of projection can be 2 4 where is angle made by incline with horizontal.
Reason : Maximum range up the incline is given by
) sin 1 ( g u2
where is angle made by incline with
horizontal..
(A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. (B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion. (C) if Assertion is true, but the Reason is false.
(D) if Assertion is false, but the Reason is true.
14. STATEMENT-1 : Two stones are simultaneously projected from level ground from same point with same
speeds but different angles with horizontal. Both stones move in same vertical plane. Then the two stones may collide in mid air.
STATEMENT-2 : For two stones projected simultaneously from same point with same speed at different
angles with horizontal, their trajectories may intersect at some point.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Answer Key (Revision Test - 02)
1. (D) 2. (C) 3. (A) 4. (A) 5. (A) 6. (B) 7. (D)
8. (D) 9. (B) 10. (B) 11. (C) 12. (a) S (b) R (c) Q (d) P
13. (D) 14. (D)
SINGLE CHOICE QUESTIONS
Time : 3 Hrs. Max. Marks : 104
Instructions :
1. For each correct single choice question 3 marks (with 1 mark negative making). 2. For each correct multiple choice question 3 marks (with 1 mark negative making). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).
1. Two blocks A & B with mass 4 kg and 6 kg respectively are connected by a stretched spring of negligible mass as in figure. When the two blocks are released simultaneously the initial acceleration of B is 1.5 m/s2 westward. The acceleration of A is :
(A) 1 m/s2 westward (B) 2.25 m/s2 eastward
(C) 1 m/s2 eastward (D) 2.75 m/s2 westward 2. System shown in figure is in equilibrium. The magnitude of change in
tension in the string just before and just after, when one of the spring is cut. Mass of both the blocks is same and equal to m and spring constant of both springs is k. (Neglect any effect of rotation) (A)
2
g
m
(B)4
g
m
(C)4
g
m
3
(D)2
g
m
3
3. In the figure a block ‘A’ of mass ‘m’ is attached at one end of a light spring and the
other end of the spring is connected to another block ‘B’ of mass 2m through a light
string. ‘A’ is held and B is in static equilibrium. Now A is released. The acceleration
of A just after that instant is ‘a’. In the next case, B is held and A is in static
equilibrium. Now when B is released, its acceleration immediately after the release is 'b'. The value of a/b is : (Pulley, string and the spring are massless)
(A) 0 (B) undefined (C) 2 (D) 2 1
4. In the figure, at the free end of the light string, a force F is applied to keep the suspended mass of 18 kg at rest. Then the force exerted by the ceiling on the system (assume that the string segments are vertical and the pulleys are light and smooth) is: (g= 10 m/s2)
(A) 60 N (B) 120 N (C) 180 N (D) 240 N (E) 200 N
5. Two massless rings slide on a smooth circular loop of the wire whose axis lies in a horizontal plane. A smooth massless inextensible string passes through the rings, which carries masses m1 & m2 at the two ends and mass m3 between the rings. If there is equilibrium when the line connnecting each ring with centre
substends an angle 300 with vertical as shown in figure. Then the ratio of masses are (A) m1 = 2m2 = m3 (B) 2m1 = m2 = 2m3 (C) m1 = m2 = m3 (D) None of these
6. Four identical metal butterflies are hanging from a light string of length 5 at equally
placed points as shown. The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle 1 and 2 is given by
1 2
(A) sin1 = 2 sin2 (B) 2cos1 = sin2
(C) tan = 2 tan (D) < and no other conclusion can be derived.
REVISION TEST - 03
COURSE : VIJAY (R)
TOPIC : NLM & Friction
SUBJECT : PHYSICS
id374296 pdfMachine by Broadgun Software - a great PDF writer! - a great PDF creator! - http://www.pdfmachine.com http://www.broadgun.com7. A bob is hanging over a pulley inside a car through a string . The second end of the string is in the hand of a person standing in the car . The car is moving with constant acceleration 'a' directed horizontally as shown in figure . Other end of the string is pulled with constant acceleration 'a' (relative to car) vertically. The tension in the string is equal to
(A) m g2 a2
(B) m g2a2 – ma (C) m g2a2 + ma (D) m(g + a)
8. A wedge of height 'h' is released from rest with a light particle P placed on it as shown. The wedge slides down an incline which makes an angle with the
horizontal. All the surfaces are smooth, P will reach the surface of the incline in time (A) 2 sin g h 2 (B) cos sin g h 2 (C) tan g h 2 (D) 2 cos g h 2
9. In the given arrangement, mass of the block is M and the surface on which the block is placed is smooth. Assuming all pulleys to be massless and frictionless, strings to be inelastic and light, R1, R2 and R3 to be light supporting rods, then acceleration of point ‘P’ will be
(Ais fixed) : (A) 0 (B) (C) m F 4 (D) m F 2
10. In the arrangement shown in the figure mass of the block B and A are 2m,, 8m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is :
(Co-efficient of friction between A and B is and pulley is ideal)
(A)
m
(B)2
1
m
(C)10
1
m
(D) 1 m 10 11. A plank is held at an angle to the horizontal (Fig.) on two fixed supports
A and B. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass m should move so that the plank does not move.
(A) g sin M m
1 down the incline (B) g sin m M
1 down the incline
(C) g sin M m
1 up the incline (D) g sin m M 1 up the incline
12. A block of mass 20 kg is acted upon by a force F = 30 N at an angle 53° with the
horizontal in downward direction as shown. The coefficient of friction between the block and the horizontal surface is 0.2. The friction force acting on the block by the ground is (g = 10 m/s2)
F 53°
(A) 40.0 N (B) 30.0 N (C) 18.0 N (D) 44.8 N
13. A particle is resting over a smooth horizontal floor. At t = 0, a horizontal force starts acting on it. Magnitude of the force increases with time according to law F = t, where is a positive constant and t is time. For the figure shown which
of the following statements is/are correct?
(A) Curve 1 shows acceleration against time (B) Curve 2 shows velocity against time (C) Curve 2 shows velocity against acceleration (D) none of these
14. An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is = 1. Assume that it can move in any
direction ; up the incline or down the incline then
=37° =1 A
(A) The maximum possible acceleration of the insect can be 14 m/sec2 (B) The maximum possible acceleration of the insect can be 2 m/sec2 (C) The insect can move with a constant velocity
(D) The insect can not move with a constant velocity
Comprehension
A block of mass M is kept in elevator (lift) which starts moving upward with constant acceleration 'b' as shown in figure. Initially elevator at rest. The block is observed by two observers A and B for a time interval t = 0 to t = T. Observer B is at rest with respect to elevator and observer A is standing on the ground.
15. The observer A finds that the work done by gravity on the block is -(A) 2 1 Mg2T2 (B) – 2 1 Mg2T2 (C) 2 1 MgbT2 (D) – 2 1 MgbT2
16. The observer A finds that work done by normal reaction acting on the block is -(A) 2 1 M(g + b)2T2 (B) – 2 1 M(g + b)2T2 (C) 2 1 M(g + b)bT2 (D) – 2 1 M(g + b)bT2 17. According to observer B
(A) The work done by gravity on the block is zero
(B) The work done by normal reaction on the block is zero (C) The work done by pseudo force on the block is zero (D) All the above are correct
Q.18 to 23
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 and Statement-2 both are False. (E) Statement-1 is False, Statement-2 is True.
18. Assertion (A) : If a body is not in rest position then the net external force acting on it cannot be zero. Reason (R) : If a body is moving with uniform speed it will continue doing so unless frictional force exceeds
the force of motion.
19. Assertion (A) : Two bodies of mass 50g and 20g are allowed to fall from the same height. If air resistance for
each is same, then both the bodies reach the earth simultaneously.
Reason (R) : Acceleration of both the bodies is same.
20. Assertion (A) : Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because of
which some movement is caused in the boat.
Reason (R) : When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction,
causing motion.
21. Assertion (A) : A bird sitting on the floor of a wire cage and cage is in the hand of a boy. Even when the bird
starts flying in the cage, the boy does not experience any change in the weight of the cage.
22. Assertion (A) : A soda water bottle is falling freely the bubbles of the gas will not rise in water. Reason (R) : Pressure in the water does not increase with depth.
23. Assertion (A) : When a ball is thrown upwards, its momentum first decreases and then increases. Reason (R) : Law of conservation of momentum is not followed is this process.
24. Figure shows a moving truck, in which there is a bob 'A' and a block 'B' attached to a spring kept on the rough floor of truck. With respect to truck, (g = 10 m/sec2) (Assume spring is massless)
(a) If bob A is in equilibrium at = 30º, the spring is in its natural state and the block B
(mass = 3 kg) is also in equilibrium , find the minimum value of the coefficient of static friction between the block and the floor of truck.
(b) If now the acceleration of truck is changed so that the new angular position of A for which it is again in equilibrium is 45º, find the minimum elongation in spring when block B is in equilibrium
assuming the value of the coefficient of static friction as that calculated in part (a).
25. Collar A starts from rest & moves to the left with a constant acceleration. Knowing that after 30 s, the relative velocity of collar B w.r.t. collar A is
900 mm/s, determine the accelerations of A and B. 26. In the arrangement shown in Figure mass of blocks A, B and C is 18.5 kg, 8 kg and 1.5 kg respectively. All the surfaces are smooth. System is released from rest at t = 0 & pulleys are light & frictionless. Calculate acceleration of block C.
27. Figure shows an ideal pulley block of mass m = 1 kg, resting on a rough ground with friction coefficient µ = 1.5. Another block of mass M = 11 kg is hanging as
shown. When system is released it is found that the magnitude of acceleration of point P on string is a. Find value of 4a in m/s2. (Use g = 10 m/s2)
28. In which of the following cases the magnitude of acceleration of the block A will be maximum (Neglection friction, mass of pulley and string)
(i) A m 2m (ii) A m 2mg (iii) A 2mg m smooth (iv) A B 2m m
Answer Key (Revision Test - 03)
1. B 2. A 3. C 4. D 5. C 6. C 7. C 8. A 9. C 10. D 11. B 12. C 13. A,B,C 14. A,C 15. D 16. C 17. D 18. D 19. D 20. D 21. D 22. A 23. A 24. (a) 3 1 (b)
31
25.
10mm/s
226. (i)
10
ms2 (ii) 0. 19 joule27. 13 28. (i) a = m 3 mg mg 2 = 3 g (ii) a = m mg mg 2 = g (iii) a = m mg 2 = 2g (iv) a = 3 g 2
REVISION TEST - 04
SUBJECT : PHYSICS
Course : VIJAY (R)
TOPIC : WPE & Circular Motion
Time : 3 Hrs. Max. Marks : 158
Instructions :
1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct multiple choice question 4 marks (with 1 mark negative marking). 3. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 4. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).
SINGLE CHOICE QUESTIONS
1. Select the correct alternative.
(A) Work done by kinetic friction on a body always results in a loss of its kinetic energy.
(B) Work done on a body, in the motion of that body over a close loop is zero for every force in nature. (C) Total mechanical energy of a system is always conserved no matter what type of internal and external forces on the body are present.
(D) When total work done by a conservative force on the system is positive then the potential energy associated with this force decreases.
2. A body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such that the block is always is in contact with the plane surfaces. Neglecting the jerk experienced at points C and B, total work done by the force is :
(A) 90 J (B) 56 J (C) 180 J (D) 0 J
3. The cart starting from rest moves down the incline. When the cart maximally compresses the spring (that is compression in the spring is maximum) at the bottom of the track, the cart’s
(A) velocity and acceleration are zero.
(B) velocity is nonzero but its acceleration is zero. (C) acceleration is nonzero, but its velocity is zero. (D) velocity and acceleration are both nonzero.
4. A horse drinks water from a cubical container of side 1 m. The level of the stomach of horse is at 2 m from the ground. Assume that all the water drunk by the horse is at a level of 2 m from the ground. Then minimum work done by the horse in drinking the entire water of the container is (Take water = 1000 kg/m
3 and g = 10 m/s2 ) : (A) 10 kJ (B) 15 kJ (C) 20 kJ (D) zero
5. A man places a chain (of mass ‘m’ and length ‘’) on a table slowly. Initially the lower end of the chain just
touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is :
(A) – mg 2 (B) – 4 mg (C) – 8 mg 3 (D) – 8 mg
6. In the track shown in figure section AB is a quadrant of a circle of 1 metre radius. A block is released at A and slides without friction until it reaches B. After B it moves on a rough horizontal floor and comes to rest at distance 3 metres from B. What is the coefficient of friction between floor and body ?
(A) 1/3 (B) 2/3 (C) 1/4 (D) 3/8
7. A particle of mass m moving along a straight line experiences force F which varies with the distance travelled as shown in the figure. If the velocity of the particle at x0 is
2
F x
0 0m
, then velocity at 4x0 is:
(A) 2 m x F 2 0 0 (B) 2 m x F0 0 (C) m x F0 0 (D) none of these
8. A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels across a rough horizontal surface with coefficient of kinetic friction , and compresses a spring with
force constant k a distance x before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane. The block travels a total distance d on rough horizontal surface. The correct expression for the maximum height h’ that the block
reaches on its return is:
(A) mgh’ = mgh – mgd (B) mgh’ = mgh + mgd
(C) mgh’ = mgh + mgd + kx2 (D) mgh’ = mgh – mgd – kx2
9. The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume
4 V
in the cube as shown. This chamber is completely filled by m kg of water. Water leaks through a hole H and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :
(A) 2 1 mg a (B) 8 3 mg a (C) 8 5 mga (D) 8 1 mga
10. A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are
a = 2 iˆ + 3 jˆ m/s2 and P = 6 iˆ
– 4ˆj kgm/s. Then the motion of the particle is
(A) uniform circular motion (B) circular motion with tangential acceleration (C) circular motion with tangential retardation (D) we cannot say anything from a and Pgiven here.
11. A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is x2 = 4ay. The wire frame is fixed and the bead can slide on it without friction. The bead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y = a is :
(A) 2 g (B) 2 g 3 (C) 2 g (D) 5 g
12. TTwo particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the strings so that they complete their circular path with equal time period is:
(A) 2 3 (B) 3 2 (C) 1 (D) None of these
13. A smooth and vertical cone-shaped funnel is rotated with an angular velocity
in such a way that an object on the inner wall of the funnel is at rest w.r.t. the funnel. If the object is slightly displaced along the slope from this position and released :
(A) it will be in equilibrium at its new position. (B) it will execute SHM
(C) it will oscillate but the motion is not SHM (D) none of these
14. A ring of radius R lies in vertical plane. A bead of mass ‘m’ can move along the ring
without friction. Initially the bead is at rest at the bottom most point on ring. The minimum constant horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle
(A) 3gR (B) 4gR (C) 5gR (D) 5.5gR
15. A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A is in horizontal direction, find the tangential force at this point in terms of tension T and mg.
(A) mg (B) T mg 2 2 ) mg ( T (C) T mg 2 2 T ) mg ( (D) mg T 2 2 T ) mg (
16. The member OA rotates about a horizontal axis through O with a constant counter clockwise velocity = 3 rad/sec. As it passes the position = 0, a
small mass m is placed upon it at a radial distance r = 0.5 m. If the mass is observed to slip at = 37º, the coefficient of friction between the mass & the
member is ______. (A) 16 3 (B) 16 9 (C) 9 4 (D) 9 5
17. A bob is attached to one end of a string other end of which is fixed at peg A. The bob is taken to a position where string makes an angle of 300 with the
horizontal. On the circular path of the bob in vertical plane there is a peg ‘B’ at
a symmetrical position with respect to the position of release as shown in the figure. If Vc and Va be the minimum speeds in clockwise and anticlockwise directions respectively, given to the bob in order to hit the peg ‘B’ then ratio
Vc : Va is equal to :
(A) 1 : 1 (B) 1 : 2 (C) 1 : 2 (D) 1 : 4
18. A disc of radius R has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length R attached to its other end as shown in figure. The disc is rotated with a constant angular velocity .
The string is making an angle 300 with the rod. Then the angular velocity of
disc is: (A) 2 / 1 R g 3 (B) 2 / 1 R 2 g 3 (C) 2 / 1 R 3 g (D) 2 / 1 R 3 3 g 2
19. An automobile enters a turn of radius R. If the road is banked at an angle of 450 and the coefficient of friction is 1, the minimum and maximum speed with which the automobile can negotiate the turn without skidding is : (A) 2 rg and rg (B) 2 rg and rg (C) 2 rg
and 2 rg (D) 0 and infinite
20. A particle is projected horizontally from the top of a tower with a velocity v0. If v be its velocity at any instant, then the radius of curvature of the path of the particle at the point (where the particle is at that instant) is directly proportional to :
(A) v3 (B) v2 (C) v (D) 1/v
MULTIPLE CHOICE QUESTIONS
21. A double conical pendulum consists of two masses, m and M, connectedby a massless string passing over a frictionless, massless pulley. The entire apparatus rotates freely at constant angular speed (rad/s) about
the vertical axis (dashed line) passing through centre of pulley as shown. After the system comes in steady state, the length of string on either sides of pulley are small and L. Pick up the correct option(s).
(A) M m cos cos (B) cos = L g 2 (C) m = ML (D) cos = 2 g
22. One of the forces acting on a particle is conservative then which of the following statement(s) are true about this conservative force
(A) Its work is zero when the particle moves exactly once around any closed path. (B) Its work equals the change in the kinetic energy of the particle
(C) Then that particular force must be constant.
(D) Its work depends on the end points of the motion, not on the path between.
23. In the figure, a block rests on the top of a smooth fixed hemispherical tube of radius R in which it can just fit. Two springs are connected to the base as shown. The block is given a small jerk so that it can slide on the hemisphere. The F-X (F is magnitude of force and x is compression) graph for the springs is given below. Which of the following may be possible :
(A) The block will compress both springs by same amount.
(B) The block will compress the springs during its to and fro motion about its original position b y different amounts.
(C) The block will perform to and fro motion along the hemispherical surface about the original position. (D) The block can never come to the original position.
Comprehension
One end of massless inextensible string of length is fixed and other end is tied to a small ball of mass m.
The ball is performing a circular motion in vertical plane. At the lowest position, speed of ball is 20g.
Neglect any other forces on the ball except tension force and gravitational force. Acceleration due to gravity is g.
24. Motion of ball is in nature of
(A) circular motion with constant speed (B) circular motion with variable speed
(C) circular motion with constant angular acceleration about centre of the circle. (D) none of these
25. At the highest position of ball, tangential acceleration of ball is
-(A) 0 (B) g (C) 5 g (D) 16 g
26. During circular motion, minimum value of tension in the string
-(A) zero (B) mg (C) 10 mg (D) 15 mg
Comprehension :
A body of mass m is moving along x-axis under the influence of conservative force with a potential energy given by U(x) = 2 2 a x cx
Where c and a are positive constants. When displaced slightly from stable equilibrium position x = x0, it will experience restoring force proportional to its displacement, the force constant being
0 x x 2 2 dx U d
27. The magnitude of force is maximum at :
(A) x = 0 (B) x = + a (C) x = – a (D) no value of x
28. The body is in stable equilibrium at
(A) x = 0 (B) x = +a (C) x = – a (D) both x = ± a
29. If body is at x = x0 where (i) x0 = 2a (ii) x0 = +a (iii) x0 = – a.
If it is displaced slightly towards right, it will experience restoring force in (A) all the three cases (B) case (ii) only
(C) case (iii) only (D) cases (i) and (ii) only.
30. Match the statements in Column with the results in Column and indicate your answer by darkening
appropriate bubbles in the 4 × 4 matrix given in the OMR.
Column – I Column – II
(a) Work done by ideal gas during free expansion (P) zero (b) A wedge block system is as shown in the fig. (Q) non zero
The wedge lying on horizontal surface is accelerated to right by a horizontal force F. All surfaces are smooth. Work done by normal reaction exerted by wedge on block in any
time interval is
(c) Two identical conducting spheres of radius 'a' are separated (R) negative by a distance 'b' (b>>a). Both spheres carry equal and
opposite charge. Net electrostatic potential energy of system of both spheres is
(d) A uniform cylinder lies over a rough horizontal platform. The (S) positive platform is accelerated horizontally as shown with acceleration
a. The cylinder does not slip over the platform.The work done
31. A particle is moving with speed v = 2t2 on the circumference of circle of radius R. Match the quantities given in column-I with corresponding results in column-II
Column-I Column-II
(A) Magnitude of tangential acceleration of particle (p) decreases with time. (B) Magnitude of Centripetal acceleration of particle (q) increases with time (C) Magnitude of angular speed of particle (r) remains constant with respect to centre of circle
(D) Angle between the total acceleration vector (s) depends on the value of radius R and centripetal acceleration vector of particle
32. In column-I condition on velocity, force and acceleration of a particle is given. Resultant motion is
described in column-II. u = initial velocity, F = resultant force and v = instantaneous velocity..
Column-I Column-II
(A) uF0
and F = constant (p) path will be circular path (B) uF0
and F = constant (q) speed will increase (C) vF0
all the time and |F| = constant (r) path will be straight line and the particle always remains in one plane.
(D) u2iˆ3ˆj and acceleration at all time a6ˆi9ˆj (s) path will be parabolic
33. Each situation in column I gives graph of a particle moving in circular path. The variables , and t represent
angular speed (at any time t) , angular displacement (in time t) and time respectively. Column gives certain
resulting interpretation. Match the graphs in column with statements in column and indicate your answer
by darkening appropriate bubbles in the 4 × 4 matrix given in the OMR.
(A) (p) Angular acceleration of particle is uniform
(B)
2
2 - graph
(q) Angular acceleration of particle is non-uniform
(C)
- t graph
t
(r) Angular acceleration of particle is directly proportional to t.
(D)
- t graph2
34. Net force on a system of particles in ground frame is zero. In each situation of column-I a statement is given regarding this system. Match the statements in column-I with the results in column-II.
Column-I Column-II
(A) Acceleration of centre of mass of system (p) is constant from ground frame
(B) Net momentum of system from ground frame. (q) is zero (C) Net momentum of system from frame of centre (r) may be zero
of mass of system
(D) K.E. of system from frame of centre of mass (s) may be constant of system
35. STATEMENT-1 : The sum of potential and kinetic energy for a system of moving objects is conserved only
when no net external force acts on the objects
STATEMENT-2 : If no nonconservative force acts on a system of objects, the work done by external forces
on a system of objects is equal to change in potential energy plus change in kinetic energy of the system. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
36. STATEMENT-1 : One end of ideal massless spring is connected to fixed
vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring.
STATEMENT-2 : To compress and to expand an ideal unstretched spring by equal amount, same work
is to be done on spring.
37. STATEMENT-1 : For a particle moving in a circular path, if direction of angular velocity and angular
acceleration is same, then angle between its velocity vector and acceleration vector increases.
STATEMENT-2 : For a particle moving in a circular path with speed increasing at constant rate, the
centripetal acceleration keeps on increasing
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True.
38. STATEMENT-1 : A cyclist is cycling on a rough horizontal circular track with increasing speed. Then the net
frictional force on cycle is always directed towards centre of the circular track.
STATEMENT-2 : For a particle moving in a circle, component of its acceleration towards centre, that is,
centripetal acceleration should exist (except when speed is zero instantaneously).
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
SUBJECTIVE QUESTIONS
39. A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant K =
4 m g
R
where 2R is the natural length of the spring. The other end of the spring is fixed to the ground at a horizontal distance 2 R from the base of the rod. The mass is released at a height of 1.5 R from ground.
(a) calculate the work done by the spring.
40. A particle is being acted upon by one dimensional conservative force. In the F–x curve shown, four points A,
B, C, D are marked on the curve. (a) State which type of equilibrium is the particle in at these positions. (b) Is the particle in equilibrium at all these points?
41. A particle of mass 2kg starts to move at position x = 0 and time t = 0 under the action of force F= (10 + 4x) N along the x-axis on a frictionless horizontal track. Find the power delivered by the force in watts at the instant the particle has moved by the distance 5m.
42. A rod AB is moving on a fixed circle of radius R with constant velocity ‘v’ as shown in figure. P is the point of
intersection of the rod and the circle. At an instant the rod is at a distance x = 5
R 3
from centre of the circle. The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.
(a) Find the speed of point of intersection P.
(b) Find the angular speed of point of intersection P with respect to centre of the circle.
43. The block of mass m initially at x = 0 is acted upon by a horizontal force F = a
bx2(where a >
mg),asshown in the figure. The co-efficient of friction between the surfaces of contact is
. The net work done on theblock is zero, if the block travels a distance of ______.
Answer Key (Revision Test - 04)
1. D 2. A 3. C 4. B 5. C 6. A 7. D 8. A 9. C 10. D 11. C 12. B 13. D 14. B 15. B 16. A 17. C 18. D 19. D 20. A 21.A,B,C,D 22. A,D 23. B,C 24. B 25. A 26. D 27. A 28. B 29. D 30. (A) p (B) q,s (C) q,s (D) q,s 31. (A) q (B) q, s (C) q, s (D) p, s 32. (A) r (B) q,s (C) p (D) q,r 33. (A) q,s (B) p (C) p (D) q,r 34. (A) p,q (B) p,r (C) p,q (D) r,s 35. D 36. D 37. D 38. D 39.
mg R
2
, 2g R
40. (a) Point A No equilibrium B Unstable equilibrium C Stable equilibrium
D Neutral equilibrium
(b) No, point A, F 0 i.e. particle is not in equilibrium
41. 300 42. (a)VP = 4 5 V (b) = R VP = R 4 V 5 43. x = [3(a – mg)/b]½
Solution will be provided with next revision test.
REVISION TEST - 05
Course : VIJAY (R)
TOPIC : CENTER OF MASS
Time : 3 Hrs. Max. Marks : 129
Instructions :
1. For each correct single choice question 3 marks (with 1 mark negative marking). 2. For each correct answer in comprehension 4 marks (with 1 mark negative marking). 3. For each correct answer in match the column 6 marks (with no negative marking). 4. For each correct assertion/reason question 3 marks (with 1 mark negative marking). 5. For each correct subjective question 6 marks (with no negative marking).
SINGLE CHOICE QUESTIONS
1. From the circular disc of radius 4R two small disc of radius R are cut off. The centre of mass of the new structure will be : (Centre of lower circular cavity lies on x-axis and centre of upper circular cavity lies on y-axis)
(A) 5 R j ˆ 5 R i ˆ (B) 5 R j ˆ 5 R i ˆ (C) 5 R j ˆ 5 R i ˆ (D) (ˆi ˆj) 14 R 3
2. The centre of mass of a non uniform rod of length L whose mass per unit length varies as =
L x . k 2
where k is a constant & x is the distance of any point on rod from its one end, is (from the same end) (A) 4 3 L (B) 4 1 L (C) L k (D) L k 3
3. Two semicircular rings of linear mass densities and 2 and of radius ‘R’ each are joined to form a
complete ring. The distance of the center of the mass of complete ring from its centre is : (A) 8 R 3 (B) 3 R 2 (C) 4 R 3 (D) none of these
4. Both the blocks shown in the given arrangement are given together a horizontal velocity towards right. If acm be the subsequent acceleration of the centre of mass of the system of blocks, then acm equals (before sliding stops at all surfaces)
(A) 0 m/s2 (B) 5/3 m/s2 (C) 7/3 m/s2 (D) 2 m/s2
5. Two men ‘A’ and ‘B’ are standing on a plank. ‘B’ is at the middle of the
plank and ‘A’ is the left end of the plank. System is initially at rest and
masses are as shown in figure. ‘A’ and ‘B’ starts moving such that the
position of ‘B’ remains fixed with respect to ground then‘A’ meets ‘B’.
Then the point where A meets B is located at :
(A) the middle of the plank (B) 30 cm from the left end of the plank (C) the right end of the plank (D) None of these
6. Two balls of same mass are released simultaneously from heights h & 2h from the ground level. The balls collides with the floor & sticks to it. Then the velocity-time graph of centre of mass of the two balls is best represented by :
(A) (B) (C) (D)
7. A cannon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum 40 Ns making an angle 30º with the original line of motion. The minimum momentum of the
other part of shell just after the burst is :
(A) 0 Ns (B) 10 Ns (C) 20 Ns (D) 17.32 Ns
8. Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipe of radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitution is 1/2 and particle 'A' starts its journey at t = 0. The time at which second collision
occurs is :
(A) s (B) 2 s (C) 5 s (D) 4 s
9. Three identical balls of mass m and radius R are placed on frictionless horizontal x-y plane. Ball A at (0, 0), Ball B at (4R, – 2 R) and ball C at (8R, – 2 2 R). Ball A is suddenly given an impulse P 2mViˆ
. If collision between balls A and B is perfectly elastic while between B and C is perfectly inelastic, then the relative velocity of ball A with respect to ball C after a long time will be:
(A) ˆj 2 2 V i ˆ 2 2 V (B) ˆj 2 2 V i ˆ 2 2 V (C) ˆj 2 2 V 3 i ˆ 2 2 V (D) ˆj 2 2 V 3 i ˆ 2 2 V
10. A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two pieces ? ( > 0)
(A) Each piece moves with speed v. (B) Each piece moves with speed v/2.
(C) One of the pieces moves with speed v/2, the other moves with speed greater than v/2 (D) Each piece moves with speed greater than v/2.
11. A trolley filled with sand is moving with a velocity v on a smooth horizontal surface due to inertia. If the sand falls off at the rate of kg/sec, the velocity of the trolley as a function of time will be best represented by :
(A) (B) (C) (D)
12. In the fig. shown a cart moves on a smooth horizontal surface due to an external constant force of magnitude F. The initial mass of the cart is M0 and velocity is zero. Sand falls on to the cart with negligible velocity at constant rate kg/s and
sticks to the cart. The velocity of the cart at time t is : (A)
F t
M
0
t
(B)F t
M
0 e t (C)F t
M
0 (D)F t
M
0
t
e t13. In the figure, the block B of mass m starts from rest at the top of a wedge W of mass M. All surfaces are without friction. W can slide on the ground. B slides down onto the ground, moves along it with a speed v, has an elastic collision with the wall, and climbs back onto W. (A) B will reach the top of W again.
(B) From the beginning, till the collision with the wall, the centre of mass of ‘B plus W’ is stationary.
(C) After the collision, centre of mass of ‘B plus W’ moves with the horizontal component of velocity
2mv
m
M
(D) When B reaches its highest position on W, the speed of W is
2mv
m
M
.
Comprehension
Figure shows block A of mass 0.2 kg sliding to the right over a frictionless elevated surface at a speed of 10 m/s. The block undergoes a collision with stationary block B, which is connected to a nondeformed spring of spring constant 1000 Nm–1. The coefficient of
restitution between the blocks is 0.5. After the collision, block B oscillates in SHM with a period of 0.2 s, and block A slides off the left end of the elevated surface, landing a distance 'd' from the base of that surface after falling height 5m. (use
2 = 10; g = 10 m/s2) Assume that the spring
does not affect the collision.
14. Mass of the block B is
(A) 0.4 kg (B) 0.8 kg (C) 1 kg (D) 1.2 kg
15. Amplitude of the SHM as being executed by block B-spring system, is
(A) 2.5 10cm (B) 10 cm (C) 3 10cm (D) 5 10cm
16. The distance 'd' will be equal to
Comprehension
Figure shows an irregular wedge of mass m placed on a smooth horizontal surface. Part BC is rough.The other part of the wedge is smooth.
17. What minimum velocity should be imparted to a small block of same mass m so that it may reach point B:
(A) 2 gH (B) 2gH (C) 2 g(Hh) (D) gh
18. The velocity of wedge when the block comes to rest (w.r.t. wedge) on part BC is :
(A) gH (B) g(Hh (C) 2 gH (D) none of these
19. If the coefficient of friction between the block and wedge is , and the block comes to rest with respect to
wedge at a point D on the rough surface then BD will be (A) H (B) h H (C) h (D) none of these Comprehension :
A smooth rope of mass m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M. The block is given a sudden kick and instantaneously acquires a horizontal velocity of magnitude V0 as shown in figure 1. As the block moves to right pulling the rope from heap, the rope being smooth, the heap remains at rest. At the instant block is at a distance x from point P as shown in figure-2 (P is a point on the rope which has just started to move at the given instant) , choose correct options for next three question.
20. The speed of block of mass M is (A) ) x L m M ( mV0 (B) x) L m M ( MV0 (C) x) L m M ( M V m 0 2 (D) ) x L m M ( m V M2 0
21. The magnitude of acceleration of block of mass M is (A) 3 2 0 3 ) x L m M ( V L m (B) 3 2 0 2 ) x L m M ( V L mM (C) 3 2 0 4 ) x L m M ( V L M m (D) 3 2 0 2 ) x L m M ( V L M
22. The tension in rope at point P is (A) 2 2 0 2 ) x L m M ( V L mM (B) 2 2 0 2 ) x L m M ( V L M m (C) 2 2 0 3 ) x L m M ( V L m (D) 2 2 0 3 ) x L m M ( V L M
23. In each situation of column-I a mass distribution is given and information regarding x and y-coordinate of centre of mass is given in column-II. Match the figures in column-I with corresponding information of centre of mass in column-II.
Column-I Column-II
(A) An equilateral triangular wire (p) xcm > 0 frame is made using three thin
uniform rods of mass per unit lengths , 2 and 3 as shown
(B) A square frame is made using (q) ycm > 0 four thin uniform rods of mass
per unit length lengths , 2,
3 and 4 as shown
(C) A circular wire frame is made (r) xcm < 0 of two uniform semicircular wires
of same radius and of mass per unit length and 2 as shown
(D) A circular wire frame is made (s) ycm < 0 of four uniform quarter circular
wires of same radius and mass per unit length , 2, 3
