1. (d) 2. (c)
3. (b) 4. (b)
5. (c) 6. (b)
7. (c) 8. (a)
9. (b) 10. (d)
11. (d) 12. (c)
13 (b) 14. (b)
15. (a) 16. (b)
17. (c) 18. (c)
19. (a) 20. (b)
Level – II
1. (c) 2. (a)
3. (a) 4. (a)
5. (c) 6. (c)
7. (b) 8. (c)
9. (c) 10. (d)
JEE ADVANCED
ONLY ONE OPTION IS CORRECT
Q.1 A ball of mass m moving with a speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest. fraction of incident energy transferred to the heavier ball is :
(A) (B) (C) (D)
Q.2 A ball of mass m moving with a certain velocity collides against a stationary ball of mass m. two balls stick with each otherduring collision. If E be initial kinetic energy, then the loss of kinetic energy in the collision is
(A) E (B) E/2 (C) E/3 (D) E/4
Q.3 Six identical balls are lined up along a straight frictionless groove. Two similar balls moving with speed v along the groove collide with this row on extreme left side end. Then :
(A) One ball from the right end will move on with speed 2v, all the other remains at rest
0.1 2gh 0.3 2gh
n
1n 2
n
(1 n) 2
2n
(1 n) 2
4n (1 n)
(B) Two balls from extreme right will move on with speed v each and the remaining balls will be at rest (C) All te balls will start moving to right with speed v/8 each
(D) All the six balls originally at rest will move on with speed u/6 each and the two incident balls will come to rest.
Q.4 A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is coefficient of restitution, then ratio of velocities of two spheres (First sphere/Second sphere) after collision will be :
(A) (B) (C) (D) .
Q.5 Two spheres A and B of equal mass are free to move on a smooth horizontal surface. A and B move towards each other with velocity vectors and respectively and collide when the line joining their centres is parallel to . After impact A and B have velocity vectors and respectively. coefficient of restitution b/w the spheres is e (< 1).
(A) b = q (B) c = r (C) a + c = p + r (D) ea = p
Q.6 A child of mass 4 kg jumps from cart B to cart A and then immediately back to the cart B. The mass of each cart is 20kg and they are initially at rest. In both cases the child jumps at 6m/s relative the cart. If the cart moves along the same line with negligible friction with the final velocities of vB and vA respectively. Find
the ratio of 6vB and 5vA.
(A) 0.5 (B) 0.75 (C) 0.25 (D) 1
Q.7 A ball rolls off a horizontal table with velocity v0 = 5 m/s . The ball bounces elastically from a vertical wall at a horizontal distance D = 8 m from the table, as shown in figure. The ball then strikes the floor a distance
x0 from the table (g = 10 m/s2). The value of x0 is :
(A) 6 m (B) 4 m (C) 5 m (D) 7 m
Q.8 A smooth sphere is moving on a horizontal surface with velocity vector immediately before it hits a
vertical wall. The wall is parallel to the vector and the coefficient of restitution between the wall and sphere is 1/3. The velocity vector of the sphere after it hits the wall is :
(A) (B) (C) (D)
Q.9 A ball of mass m collides perpendicularly on a smooth stationary wedge of mass M. If the coefficient
of restitution of collision is e, the velocity of the wedge after collision is :
(A) (B) (C) (D)
Q.10 Two masses A and B connected with an inextensible string of v m/s along the ground perpendicular to line AB as shown in figure. Find the tension in string during their subsequent motion.
(A) (B)
(C) (D)
Q.11 Four particles of mass 5, 3, 2, 4 kg are at the points (1, 6), (–1, 5), (2, –3), (–1, – 4). Find the coordinates of their centre of mass.
(A) (1/7, 23/14) (B) (1/4, 23/14) (C) (1/7, 13/14) (D) (2/7, 13/14) Q.12 A semicircular portion of radius 'r' is cut from a uniform rectangular plate as shown
in the figure. The distance of centre of mass C of remaining plate from O is :
(A) (B)
(C) (D)
Q.13 Bullets of mass 109 each are fired from a machine gun at rate of 60 bullets/minute. The muzzle velocity of bullets is 100 m/s. The thrust force due to firing bullets experienced by the person holding the gun stationary is
(A) 2N (B) 3N (C) 5N (D) 1N
m v
0q M
(1 e) m v
0M
e m v
0M m
M v e
0M m
0 2
(1 e) m v sin M m sin
q
q
m
2m
A v
B
2mv
23
mv
23
mv 2 2mv
2C O
2r 3
3r 2(4 )
2r 4
2r
3(4 )
Q.14 A body of mass M (fig) with a small disc of mass m placed on it rests on a smooth horizontal plane. disc is set in motion in horizontal direction with velocity v. To what height (relative to the initial level) will the disc
rise after breaking off body M? friction is assumed to be absent.
(A) (B) (C) (D)
Q.15 If a ball is thrown upwards from the surface of earth:
(A) earth remains stationary while ball moves upwards (B) ball remains stationary while earth moves downwards (C) ball and earth both moves towards each other
(D) ball and earth both move away from each other
Q.16 In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where ‘R’ is mean radius of tube). Assume that the tube
remains in vertical plane.
(C) R/2 (D) R
Q.17 A spaceship is moving with constant speed v0 in gravity free space along + Y-axis suddenly shoots out one third of its part with speed 2v0 along + X-axis. Find the speed of the remaining part.
(A) (B) (C) (D)
Q.18 Three particles A, B and C each of the same mass m and connected by strings AB and BC of length a lie at rest with the string in a straight line on a smooth horizontal table. B is projected with a speed v0 at right angles to AB. Find the speed of particles A relative to C at the moment it collides with particle C.
(A) (B) (C) (D)
Q.19 A ball is dropped from a height of 1m. The coefficient of restitution between the ground and the ball is 1/3.
The height to which the ball will rebound after two collisions with ground is
(A) (1/81) m (B) (1/27) m (C) (1/36) m (D) (1/45) m
Q.20 A moving body with a mass m1 strikes a stationary body of mass m2. The masses m1 and m2 should be in the ratio m1/m2 so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact.
Then the ratio m1/m2 is
(A) 1/25 (B) 1/5 (C) 5 (D) 25
m v
M
mv2
2g Mm
mv2
g Mm
mv2
3g Mm
2mv2
3g Mm
m
m R
0
3v
2 0
13v
4 0
13v
2 0
5v 2
v0
A B C
0
1 v
3
04 v
3
02 v
3
02 v
5
Q.21 Two small bodies of masses 'm' and '2m' are placed in a fixed smooth horizontal circular hollow tube of mean radius 'r' as shown.
The mass 'm' is moving with speed 'u' and the mass '2m' is stationary. After their first collision, the time elapsed for next collision is : [ coefficient of restitution e = 1/2 ]
(A) (B) (C) (D)
Q.22 Two balls of equal masses are projected upward simultaneously, one from the ground with speed 50 m/s and other from a 40 m high tower with initial speed 30 m/s. Find the maximum height attained by their centre of mass.
(A) 50m (B) 25m (C) 100m (D) 75m
Q.23 A small steel ball A is suspended by an inextensible thread vertically downwards such that its surface remain just in contact with thread during downward motion and collides elastically with the suspended ball. If the suspended ball just completes vertical circle after collision, calculate the velocity (in cm/s) of the falling ball just before collision. (g
= 10 m/s2)
(A) 625 (B) 1250 (C) 500 (D) 750
Q.24 Two particles of mass 1 kg & 0.5 kg are moving in same direction with speed of 2m/s and 6m/s respectively on a smooth horizontal surface. speed of centre of mass of system is :
(A) 10/3 m/s (B) 10/7 m/s (C) 11/2 m/s (D) 12/3 m/s
Q.25 A bullet of mass m strikes an obstruction and deviates off at 60° to its original direction. If its speed is also changed from u to v, find the magnitude of the impulse acting on the bullet.
(A) (B) (C) (D)
(C) R/2 (D) R
2 r u
4 r
u
3 r
u
12 r
u
A B
O
2 2
m u uv v m u
2 2uv v
2m u 2 uv v 2
2 2
m u uv 2v
Q.26 All the particles of a body are situated at a distance R from origin. distance of centre of mass of the body from the origin is :
(A) = R (B) (C) > R
Q.27 In the arrangement shown in the figure, mA = 2 kg and mB = 1 kg.
String is light and inextensible. Find the acceleration of centre of
mass of both the blocks. Neglect friction everywhere.
(A) g/9 upwards (B) g/9 downwards (C) g/7 downwards (D) g/7 upwards
Q.28 Water flows through a pipe bent at an angl
by water on the bend of the pipe of area of cross section S ?
(A) (B) (C) (D)
Q.29 A block of mass 2 kg slides along a frictionless table with a speed of 10m/sec. Directly in front of it and moving in the same direction is a block of mass 5 kg moving at 3 m/sec. A massless spring of spring constant k = 1120 N/m is attached to the back side of 5 kg mass as shown in figure. When the blocks collide the maximum compression in the spring (if the spring does not bend) will be
(A) 0.25 m (B) 0.4 m (C) 0.33 m (D) 1.12 m
Q.30 A body moving towards a finite body at rest collides with it it is possible that
(a) both the bodies come to rest (B) both bodies move after collision (c) the moving body comes to rest & stationary body starts moving
(d) the stationary body remains stationary, moving body changes its velocity
(A) a, b only (B) c, d only (C) a, c, d (D) a, b, c, d
Q.31 A ball hits a floor and rebounds after an inelastic collisionn. In this case
(A) momentum of ball just after the collision is same as that just before the collision (B) mechanical energy of ball remains the same during the collision
(C) total momentum of ball and the earth is conserved (D) None of these
Q.32 When two particles of masses m1 and m2 are moving under the action of their internal forces and –
under the force
//////////////
A
B
2 v Scos
2 2 v Ssin 2 2 v S sin
2 2 2 v Ssin cos
2
f 1 f 2
1 2
1 2
m m m m
f1
(B) Their relative motion is the same as that of one of the particles with its mass replaced by the reduced mass of the system, with the other particle remaining at rest.
(C) Their relative motion can be obtained by assuming one of the particles to have an infinite mass and by replacing the mass of the second particle by the reduced mass of the system, the force between them of the same as before
(D) Both the particles move with uniform velocity.
Q.33 An electron of mass m moving with a velocity v collides head on with an atom of mass M. As a result of the collision a certain fixed amount of energy is stored internally in the atom. The minimum initial velocity possessed by the electron is :
(A) (B) (C) (D) None of these
Q.34 A hand ball falls on the ground and rebounds elastically along the same line peratining to motion. Then (A) The linear momentum is conserved
(B) The linear momentum is not conserved, the loss in momentum being dissipated as heat in the ball and the ground
(C) During the collision the full kinetic energy of the ball is converted into potential energy and then is completely converted to kinetic energy of the ball
(D) None of these
Q.35 Choose the correct statement –
(A) The relative velocity of two particles in a head on collision is unchanged both in magnitude and direction (B) The linear momentum is conserved but not the kinetic energy in elastic collisionn.
(C) A quick collision between two bodies is more violent than a slow collision even though the initial and final velocities are identical
(D) None of these
Q.36 A particle of mass m makes a head-on elastic collision with a particle of mass 2m initially at rest. The velocity of the first particle before and after collision is given to be u1 and v1. Then which of the following statements is true in respect of this collision ?
(A) For all values of u1, v1 will always be less than u1 in magnitude and |v1| = u1/3 (B) The fractional loss in kinetic energy of the first particle is 9/8
(C) The gain in kinetic energy of the second particle is (8/9)th of the initial kinetic energy of the first particle.
(D) There is a net loss in the energy of the two particles in the collision.
Q.37 Hail storms are observed to strike the surface of the frozen lake at 30° with the vertical and rebound at 60°
with the vertical. Assume contact to be smooth, the coefficient of restitution is :
(A) (B) e = 1/3 (C) (D) e = 3
Q.38 If the external force acting on a system has zero resultant the centre of mass
(A) Must not move (B) Must not accelerate (C) May accelerate (D) None of these Q.39 Which one of the following statements does not hold good when two balls of masses m1 and m2 undergo
elastic collision
(A) When m1 < m2 and m2 at rest, there will be maximum transfer of momentum.
(B) When m1 > m2 and m2 at rest, after collision ball of mass m2 moves with four times the velocity of m1. (C) When m1 = m2 and m2 at rest, there will be maximum transfer of K. E.
(D) When collision is oblique & m2 at rest with m1 = m2 after collision the ball moves in opposite directions.
Q.40 A small sphere of mass m = 1 kg is moving with a velocity m/s. It hits a fixed smooth wall and rebound with velocity m/s. The coefficient of restitution between the sphere and the wall is n/16. Find value of n.
(A) 6 (B) 7 (C) 4 (D) 9
Q.41 A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. two particles coalesce on collision. The new particle of mass 2m will move in the north-eastern direction with a velocity
Mm Δ E m M
2
M 2 M Δ m E m 2 M Mm m Δ E
e 1/ 3 e 3
(4i ˆ ˆ - j)
(A) –v/2 (B) v/2 (C) (D) None Q.42 Internal forces can change
(A) linear momentum but not kinetic energy of the system.
(B) kinetic energy but not linear momentum of the system.
(C) linear momentum as well as the KE of system.
(D) neither linear momentum, nor kinetic energy of system.
Q.43 Two particles of equal mass have initial velocities and . First particle has an acceleration (
) m/s2, while the acceleration of the second particle is zero. The centre of mass of the two particles moves in :
(Aa) circle (B) parabola (Cc) ellipse (D) straight line
Q.44 Two colliding particles of masses m1 and m2 moving with v1 and v2 –1= m1–1 + m2–1 and is the coefficient of restitution)
(A) Loss of kinetic energy of (1– )2 (B) Loss of potential
energy of
) (v1 + v2) ) (v1 + v2)
Q.45 A bullet of mass 0.01 kg, travelling at a speed of 500 ms–1, strikes a block of mass 2 kg, which is suspended by a string of length 5 m, & emerges out. block rises by a vertical distance of 0.1 m. The speed of the bullet after it emerges from the block is
(A) 55 ms–1 (B) 110 ms–1 (C) 220 ms–1 (D) 440 ms–1
Q.46 An anti-air craft shell has been fired and it has kinetic energy K. It explodes in mid air. The sum of kinetic energies of particles is-
(A) K (B) < K (C) > K (D) 0
Q.47 A radioactive nucleus initially at rest decays by emitting an electron and an anti-neutrino at right angles to one another. The momentum of the electron is 3.2 × 10–23 kg-ms–1 and that of anti-neutrino is 6.4 × 10–23 kgms–1. The direction of recoiling nucleus with that of e– is-
(A) tan–1 (1/2) (B) tan–1 (2) (C) tan–1 – tan–1 2
Q.48 A neutron travelling with a velocity v and kinetic energy E collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of the total energy retained by neutron is :
(A) (B) (C) (D)
Q.49 Figure shows an irregular wedge of mass m placed on a smooth horizontal surface.
Part BC is rough. What minimum velocity should be imparted to a small block of
same mass m so that it may reach point B –
(A) (B)
(C) (D)
v / 2
2i m / s ˆ 2 jm / s ˆ
ˆ ˆ i j
1 2
21/ 2 v v
1 2 2 2
1/ 2v v 1
A A
F
H G IK 1 J 2 A
A
F
H G IK 1 J
2F A A
H G IK 1 1 J
2 AA
F
H G IK
11J
2m m
H wedge B
b
C
2 gH 2gH
2 g (H
h) gh
Q.50 In the above question, the velocity of wedge when the block comes to rest on part BC is –
(A) (B) (C) (D) None of these
Q.51 The diagram shows the velocities just before collision of two smooth spheres of equal radius and mass. The
impact is perfectly elastic. The velocities just after impact are :
(A) (B)
(C) (D)
Q.52 Choose incorrect one. If no external force acts on a system :
(A) Velocity of centre of mass remains constant (B) Velocity of centre of mass is not constant (C) Velocity of centre of mass may be zero (D) Acceleration of centre of mass is zero.
Q.53 A system consists of mass M and m(<M). The centre of mass of the system is ;
(A) At the middle (B) Nearer to M (C) Nearer to m (D) At the position of large mass.
Q.54
is initially at rest on a horizontal frictionless surface. Just after firing, the centre of mass of the gun-shot system :
(A) moves with a velocity Vm/M (B) moves with a velocity horizontal direction
(C) remains at rest (D) moves with a velocity in the
horizontal direction.
Q.55 Two persons standing on a floating boat run in succession along its length with a speed 4.2 m/s relative to the boat and dive off from the end. The mass of each man is 80kg and that of boat is 400kg. If the boat was initially at rest, find final velocity of boat. Neglect friction –
(A) 0.6 m/s (B) 0.7 m/s (C) 0.1 m/s (D) 1.3 m/s
Q.56 A thin uniform wire is bent to form the two equal sides AB and AC of triangle ABC, where AB = AC = 5cm.
The third side BC of length 6 cm is made from uniform wire of twice the density of the first. The distance of centre of mass from A is :
(A) (34/11) cm (B) (11/34) cm (C) (34/9) cm (D) (11/45) cm
Q.57 A ball is dropped from a height h on ground. If coefficient of restitution is e, height to which ball goes up after is rebounds for the nth time is
(A) h e2n (B) h en (C) e2n/h (D) h/e2n
Q.58 Two particles of mass 1 kg & 0.5 kg are moving in same direction with speed of 2 m/s and 6 m/s respectively on a smooth horizontal surface. speed of centre of mass of system is :
(A) 3.33 m/s (B) 4 m/s (C) 5.5 m/s (D) 5 m/s
gh g (H h) 2 gH
Vm M
M m
m M V
Q.59 A block of mass M is tied to one end of a massless rope. other end of rope is in hands of a man of mass 2M as shown in figure. The block and the man are resting on a rough wedge of mass M as shown in the figure.
The whole system is resting on a smooth horizontal surface. The man pulls the rope. Pulley is massless and frictionless. What is displacement of wedge when the block meets pulley. (Man does not leave his position during the pull) ?
(A) 0.5 m (B) 1 m (C) zero (D) (2/3)
Q.60 A t = 0, the positions and velocities of particles are as shown in figure. They are kept on a smooth surface and being mutually attached by gravitational force. Find the position of centre of mass at t = 2s :
(A) X = 5 m (B) X = 7 m (C) X = 3 m (D) X = 2 m
Q.61 horizontal direction. At highest
point in its trajectory it explodes into two pieces of equal mass. One of pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is-
(D) (
Q.62 A particle of mass 1 kg moving with a velocity of 5m/s collides elastically with rough ground at
with vertical as shown. What can be the minimum coefficient of friction between the particle and the ground
(A) 1 (B) 0.5 (C) 0.75 (D) 0.25
Q.63 Consider the following two statements
(a) Linear momentum of the system remains constant (b) Centre of mass of the system remains at rest.
(A) a implies b and b implies a (B) a does not imply b and b does not imply a (C) a implies b but b does not imply a (D) b implies a but a does not imply b.
Q.64 A particle at rest suddenly disintegrates into two particles of equal masses which start moving The two fragments will-
(A) Move in the same direction with equal speeds (B) Move in any directions with any speed
(C) Move in opposite directions with equal speeds (D) Move in opposite directions with unequal speeds Q.65 In a free space, a rifle of mass ' M' shoots a bullet of mass 'm' at a stationary block of mass M distance 'D'
away from it. When bullet has moved through a distance 'd' towards the block, the centre of mass of the bullet block system is at a distance of
3 2
//////////////////////////////////////////////////
q
(a) from the block (b) from the rifle (c)
from the rifle (d) from the bullet
(A) b, c (B) a, d (C) a, b, c (D) a, b
Q.66 A body has its centre of mass at origin. The x-coordinates of particles (A) May be all positive (B) May be all negative
(C) May be all non-negative
(D) May be +ve for some cases & negative in other cases
Q.67 A train of mass M is moving on a circular track of radius R with constant speed V. length of train is half of the perimeter of track. The linear momentum of train will be –
(A) 0 (C) MVR (D) MV
Q.68 Two particles A and B initially at rest move towards each other under a mutual force of attraction. The speed of centre of mass at the instant when the speed of A is v and the speed of B is 2v is :
(A) v (B) Zero (C) 2v (D) 3v/2
Q.69 A ball of mass 50 gm is dropped from a height h = 10 m. It rebounds losing 75 percent of its kinetic energy.
If it remains in contact with th
(A) 1.3 N-s (B) 1.05 N-s (C) 1300 N-s (D) 105 N-s
Q.70 The area of F-t curve is A, where 'F' is the force on one mass due to the other. If one of the colliding bodies of mass M is at rest initially, its speed just after the collision is :
(A) A/M (B) M/A (C) AM (D)
Q.71 A 500 kg boat has an initial speed of 10 m/s as it passes under a bridge. At that instant a 50 kg man jumps straight down into the boat from the bridge. The speed of the boat after the man and boat attain a common speed is
(A) 100/11 m/s (B) 10/11 m/s (C) 50/11 m/s (D) 5/11 m/s
Q.72 Consider a system of two identical particles. One of particles is at rest and the other has an acceleration . The centre of mass has an acceleration –
(A) zero (B) (C) (D)
Q.73 A man of mass m climbs on a rope of length L suspended below a balloon of mass M. balloon is stationary with respect to ground. If man begins to climb up rope at a speed vrel (relative to rope). In what direction and with what speed (relative to ground) will the balloon move
(A) downward, (B) upwards, (C) downwards, (D) downwards,
Q.74 Two particles A and B start moving due to their mutual interaction only. If at any time 't', and are their respective accelerations, and are their respective velocities, and upto that time WA and WB are the work done on A and B respectively by the mutual force, mA and mB are their masses respectively, then which of the following is always correct –
(A) (B) (C) (D)
Q.75 The rotational analogue of force in linear motion is :
Q.75 The rotational analogue of force in linear motion is :