A particle is moving in a radius $$R$$ with constant speed $$v$$. The magnitude of average acceleration after half revolution is

A mass is whirled in a circular path with constant angular velocity and its linear velocity is $v$. If the string is now halved keeping the angular momentum same, the linear velocity is

A body of mass $m$ is performing a UCM in a circle of radius $r$ with speed $v$. The work done by the centripetal force in moving it through $\left(\frac{2}{3}\right) \mathrm{rd}$ of the circular path is

In U.C.M., when time interval $\delta t \rightarrow 0$, the angle between change in velocity ( $\delta \mathbf{v}$ ) and linear velocity $(\boldsymbol{v})$ will be