$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod. The acceleration of the centre of mass of the rod is:

In a system,two particles of masses $m_1 = 3 \text{ kg}$ and $m_2 = 2 \text{ kg}$ are placed at a certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance of $2 \text{ cm}$. In order to keep the center of mass of the system at the original position,the particle of mass $m_2$ should move towards the center of mass by a distance of . . . . . . $\text{cm}$.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: When a firecracker (rocket) explodes in mid-air,its fragments fly in such a way that the centre of mass of the fragments continues to move along the same parabolic path that the firecracker would have followed had it not exploded.
Reason $(R)$: The explosion of a firecracker (rocket) occurs due to internal forces only,and no external force acts to cause this explosion.

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The displacement of the centre of mass of the $A+B$ system until the string becomes vertical is

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The distance moved by the man with respect to ground is

As shown in the figure,two blocks are connected with a light spring. When the spring is at its natural length,velocities are given to them as shown in the figure. Choose the wrong alternative.