Newton's laws for System of Particles

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

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

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. 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 $\theta$ in the horizontal direction
3. Remains at rest
4. moves with a velocity $\frac{v(M-m)}{(M+m)}$ in the horizontal direction.

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 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. 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.

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. $\left(\frac{g(m_2+m_1{)}^2}{(m_1-m_2{)}^2}\right)$

2. $(m_1+m_2)g$

3. $\left(\frac{(m_2-m_1{)}^{2}g}{(m_1+m_2{)}^2}\right)$

4. $\left(\frac{g(m_1+m_2{)}^2}{\left(2m_1{m}_2\right)}\right)$