Target IIT JEE 2007
PHYSICS
Daily Practice Problems CLASS: XI (P, Q, R, S) DATE: 26-27/09/2005 DPP NO.-57 TIME :1 HOUR MAX. MARKS: 69 [Deduct one mark for each wrong Answer in the following question in which only one is correct ]
[23x3=69]
Q. 1 A person initially at point P in the illustration stays there for some time and then moves along the axis to Q and stays there for some time. She then returns quickly to R, stays there for some time, and then strolls slowly back to P. Circle the position vs. time graph below that best represents this motion?
Q R P Q.2 Two particles are projected simultaneously from two points O and O' such that
10 m is the horizontal and 5 m is the vertical distance between them as shown in the figure. They are projected at the same inclination 60° to the horizontal with the same velocity 10 ms~!. The time after which their separation becomes minimum is
(A) 2.5 sec (B) 1 sec (C) 5 sec (D) 10 sec Question No. 3 to 12
Apendulum bob has mass m. The length of pendulum is /. It is initially at rest. Aparticle Pof-^- moving horizontally along -ve x-direction with velocity -/2g7 collides with the bob and comestorest. When the bob comes to rest, another particle Q of mass nyrioving horizontally along y direction collides with the bob and sticks to it. It is observed that the bob now moves along a horizontal circle. There is horizontal floor 21 distance below the point of suspension of the pendulum.
Q. 3 For the first collision which quantity is conserved:
Q.7
(A) Only mechanical energy
(C) Both (B) Only momentum
(D) None Q. 4 Tension in string immediately after the first collision
(A) 2mg (B)mg ( Q ^ m g
Q. 5 Tension in string just before the second collision
(A)^mg mg
<C> l l
( D ) | m g
( D ) —V3 m g Q. 6 The height of the circular path above the floor is:
(A) 31
( B ) f 51
<Q T (D) Data not sufficient Which of the following is a possible value of the speed of particle Q just before its collision with the bob:
(Tig _ (C) J ~ (D) None 3 / g
( A )V 4
Time period of the circular motion:
T ' f j f 7 f j f l [JT (A) 2 n j - ( B ) 2 t c ^ — ( C ) 2 ^ — ( P ) 2 x y4 g
Q.9 Magnitude ofthe net force on the particle during its circular motion 1 Ff ' 2 J l 8
(A) —j- mg ( B ) — mg ( Q j m g (D)none Q. 10 Magnitude of average acceleration during half part Of its circular motion
^
Q.ll If the string breaks during the circular motion, the bob will hit the floor after a time:
[51 [41 [47 ( A ) ^ (B) ^ (D) none
Q. 12 Distance of the point where the particle hits the floor from the vertical line through the point of suspension.
?' < c >JS
( A ) J f / ( B ) J f / ( C ) M * (D)none Question No. 13 to 17
In the figure shown a long cart mo ves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling from a stationary hopper on to the cart with negligible velocity at constant rate p, kg/s and sticks to the cart.
After time t0 the sand starts leaking from the bottom at the same constant rate |i kg/s. Eventually at time t = 2t0 the sands stops falling from the hopper on to the cart and force F also stops acting.
Q.13 The velocity ofthe cart at time t(<t0)
Ft Ft „t
Ft Ft L0- I—*F
M0+(atC M0 + ut
Q. 14 In the same model of the above question if the cart is to be moved with constant velocity v, then th<
power supplied by external agent applying that force is
(A)2|iv (B) (tv (C) IIV2 (D) j nv2
Q.15 In the above question the rate ofincrease ofthe kinetic energy ofthe cart (with sand) is
(A) 2 (iv2 (B) (iv (C) (iv2 (D) | (iv2
Q. 16 In the above model (for t0 < t < 2t0) what extra force is required to move the cart with the speed acquired at t0
(A) (iv towards right (B)2(iv towards right (C)zero (D) |iv towards left Q. 17 In the above model at t = 3t0 the momentum of cart and remaining sand in the cart is
Ftp
M0+2(it0 (B) 2Ft0
Q. 18 Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time ti. Which graphs show an object whose speed is increasing for the entire tune interval between ti and til
\ III
(A) graph I, only (C) graphs I and in, only
(B) graphs I and II, only (D) graphs I, II, and III Q. 19 A wheel comprises of a ring having mass 2m and two rods (mass m and
length I) along two diameters as shown. Find moment of inertia of the wheel about an axis passing through point P and perpendicular to the plane of wheel.
(A) f i n * (B)fm/2 (C) ~mP (D)none
Q.20
Q.21
A square of side L/2 is removed from one corner of a square sandwich that has sides oflength L. The center of mass of the ramainder of the sandwich moves from C to C'. The displacement of the x-coordinate of the center of mass (from C to C) is
( O ^ L
a
.f<A>T2L ® # L
Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than (rc/2)R, (one quarter circle) the center of mass of the two cars
(A) remains at the initial point
(B) travels along a diameter of the circle at speed < v (C) travels along a diameter of the circle at speed = v (D) travels along a diameter of the circle at speed > v Q. 22 The graph shows position as a function of time for two trains
running on parallel tracks. Which statement is true?
(A) At time tB, both trains have the same velocity.
(B) Both trains have the same velocity at some time after tB
(C) Both trains have the same velocity at some time before tB. (D) Somewhere on the graph, both trains have the same acceleration.
position
time
Q. 23 End A of a vertical uniform light rod, is attached to a frictionless pivot and a sphere ofmass 2M hangs at other end B. At some instant of time a strong wind begins to apply a constant horizontal force toB.Asa result, the dumbbell rotates about A in a vertical plane. The speed of B at the instant when the dumbbell is horizontal is
Ov ?
Q.18
I 2 t
II
1 2
}
(A) graph I, only (C) graphs I and ffl, only Q.19 A
Q.22 The graph shows (A) At time tB, bothl (B) Both trains have the samei
(C) Both trains have the same velocity at some time before tB.
•(D)!
Q.23 End A of a vertical