Centreofmass Wa

PRACTICE TEST Q.1

PHYSICS

 A particle of mass 15 kg has an initial velocity v1  ˆi  2ˆj m/s. It collides with another body and  the impact time is 0.1 s, resulting in a velocity v t  6ˆi  4ˆj  5kˆ m/s after impact. The average force of impact on the particle is : (A) 15 15ˆi  6ˆj  5kˆ N (B) 15 5ˆi  6ˆj  5kˆ N





 (C) 1505ˆi  6ˆj  5kˆ N







(D) 150 5ˆi  6ˆj  5kˆ N

Q.2

A ball is dropped h m above the floor if e is the coefficient of restitution, then after collision it rebounds to a height of (A) eh (B) e2h (C) e3h (D) (1 + e)h

Q.3

After a completely inelastic collision, two objects of the same mass and same initial speed are found to move away together at half their initial speed. The angle between the initial velocities of the object is : (A) 120° (B) 90° (C) 60° (D) none of these.

Q.4

Two skaters A and B of mass 50 kg and 70 kg respectively stand facing each other 6 cm apart. They then pull on a rope stretched between them. How far has each moved when they meet (A) both have moved 3 m (B) A moves 2.5m and B 2.5 m (C) A moves 3.5 m and B 2.5 m (D) A moves 2 m and B 4 m

Q.5

A ball falls vertically onto a floor, with momentum P, and then bounces repeatedly. The coefficient of restitution is e. The total momentum imparted by the ball to the floor is : (A) p(1 + e)

Q.6

p 1 e

 1 (C) p1    e

1 e   (D) p 1 e 

A particle of mass m moving with velocity u makes an elastic one- dimensional collision with a stationary particle of mass m. They are in contact for a very brief time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is :

(A) mu/T

mk

(B)

(B) 2mu/T

(C) mu/2T

CENTRE OF MASS

(D) none of these.

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PHYSICS PRACTICE TEST Q.7 A particle strikes a horizontal frictionless floor with a speed u, at an angle  with the vertical, and rebounds with a speed v, at an angle  with the vertical. The coefficient of restitution between the particle and the floor is e. The magnitude of v is:

(A)

eu

(C) u sin 2   e 2 cos 2  Q.8

mk

(D)

u e 2 sin 2   cos 2 

v  2gh

(B)

 m v  2gh 1    M

  M  (C) v  2gh 1      m 

(D)

  m  v  2gh 1      M 

Two particles of mass M and 2M are at a distance D apart. Under their mutual gravitational force they start moving towards each other. The acceleration of their centre of mass when they are D/ 2 apart is : (A)

Q.10

(1 - e)u

A bullet of mass m hits a target of mass M hanging by a string and gets embedded in it. If the block rises to a height h as a result of this collision, the velocity of the bullet before collision is : (A)

Q.9

(B)

2GM D

2

(B)

4GM D

2

(C)

8GM D2

(D) zero.

A block of mass M is attached with a spring of spring constant K. The whole arrangement is placed on a vehicle as shown in the figure. If the vehicle starts moving towards right with an acceleration a (there is no friction anywhere), then (A) maximum elongation in the spring is Ma/K (B) Maximum elongation in the spring is 2Ma/K (C) Maximum compression in the spring is 2Ma/K (D) None of these.

CENTRE OF MASS

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PHYSICS PRACTICE TEST Q.11 A body is fired from point P and strikes at Q inside a smooth circular wall as shown in the figure. It rebounds to point S (diametrically opposite to P), then

Q.12

(A) The coefficient of restitution is zero

(B) The coefficient of restitution is 1

(C) Kinetic energy is not conserved

(D) The coefficient of restitution is 1/

3.

A particle of mass m moving with a speed v collides elastically with another particle of mass 2m on a horizontal circular tube of radius R, then select the correct alternative(s).

2R v (B) The time after which the next collision will take place is directly proportional to m (C) The tie after which the next collision will take place is inversely proportional to m. (D) None of these.

(A) The time after which the next collision will take place is

Q.13

A block of mass M is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass 2M as shown in the 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 mass less and frictionless. What is the displacement of the wedge when the block meets the pulley. (Man does not leave his position during the pull)

(A) 0.5 m Q.14

mk

(B) 1 m

(C) zero

(D) 2/3 m.

If no external force acts on a system then which statement is wrong. (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. CENTRE OF MASS

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PRACTICE TEST Q.15 If a ball collides elastically with a smooth horizontal floor, then

(A) 

(B) u = v

(C) 

PHYSICS

(D) u > v

ANSWER KEY Q.1 Q.8 Q.15

mk

B C AB

Q.2 Q.9

B D

Q.3 Q.10

A B

Q.4 Q.11

C B

Q.5 Q.12

CENTRE OF MASS

D A

Q.6 Q.13

B A

Q.7 Q.14

C ACD

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