$(a)$ Is it possible that a body is in accelerated motion under the action of a force,yet no work is being done by the force? Explain with an example.
$(b)$ Two bodies of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. What is the ratio of their linear momenta?

(N/A) Yes,it is possible in the case of a body moving in a circular path with a constant speed $v$. The body experiences a centripetal acceleration directed towards the center of the circular path. The displacement is always tangential to the circular path,meaning the angle between the force and the displacement is $\theta = 90^{\circ}$. Thus,the work done is:
$W = F S \cos 90^{\circ} = 0$.
$(b)$ We know that the relation between kinetic energy $K$ and linear momentum $p$ is given by $p = \sqrt{2 m K}$.
For two bodies with equal kinetic energies $K$:
$p_{1} = \sqrt{2 m_{1} K}$
$p_{2} = \sqrt{2 m_{2} K}$
Therefore,the ratio of their linear momenta is:
$\frac{p_{1}}{p_{2}} = \sqrt{\frac{2 m_{1} K}{2 m_{2} K}} = \sqrt{\frac{m_{1}}{m_{2}}}$.