Newton's Laws for System of Particles

Q.

Consider the following two statements:
(A) Linear momentum of the system remians constant. (B) Centre of mass of the system remains at rest.

1. A does not imply B and B does not imply A.

2. A implies B and B implies A.

3. A implies B but B does not imply A.

4. B implies A but A does not imply B.

Q. A loaded spring gun of mass 'M' fires a bullet of mass 'm' with a velocity 'v' at an angle of elevation θ. The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun­–bullet system

1. Moves with a velocity v m/M
2. moves with velocity vm/M cos in the horizontal direction
3. moves with a velocity in the horizontal direction.
4. Remains at rest

Q. Figure below shows two blocks of masses 5 kg and 2 kg placed on a frictionless surface and connected with a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. Deduce (a) velocity gained by the centre of mass and (b) the separate velocities of the two blocks in the centre of mass coordinates just after the kick.

1. 10 m/s, 14 m/s, 10 m/s
2. 10 m/s, 4 m/s, 10 m/s
3. 10 m/s, 4 m/s, -10 m/s
4. 10 m/s, 10 m/s, 10 m/s

Q.

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the acceleration of the centre of mass of the two blocks.

1. 

2. 

3. 

4. g

Q. Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. The magnitude of acceleration of the centre of mass of the two blocks is ___.

Q. Figure below shows a fixed wedge on which two blocks of masses 2 kg and 3 kg are placed on its smooth inclined surfaces. When the two blocks are released from rest, find the acceleration of centre of mass of the two blocks.

1. g
2. $\frac{\sqrt{31}g}{10}$
3. g/2
4. g/5

Q.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_1$ and $m_2$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

1. 

2. 

3. 

4. 

Q. A uniform rod of mass 'm' and length 'L' is tied to a vertical shaft. It rotates in horizontal plane about the vertical axis at angular velocity $\omega$. How much horizontal force does the shaft excert on the rod?

1. $m{w}^{2}L$
2. $\frac{M{w}^{2}L}{2}$
3. $\frac{m{w}^{2}L}{4}$
4. $zero$

Q.

Consider the following two statements:
(A) Linear momentum of a system of particles is zero.
(B) Kinetic energy of a system of particles is zero.

1. A implies B and B implies A.

2. A does not imply B and B does not imply A.

3. A implies B but B does not imply A.

4. B implies A but A does not imply B.

Q.

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

1. Linear momentum of the system does not change in time.

2. Kinetic energy of the system does not change in time.

3. Angular momentum of the system does not change in time.

4. Potential energy of the system does not change in time.