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
A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in $\mathrm{m} / \mathrm{s}^2$ is
A stone of mass 1 kg is tied to a string 2 m long and it's rotated at constant speed of $40 \mathrm{~ms}^{-1}$ in a vertical circle. The ratio of the tension at the top and the bottom is [Take $g=10 \mathrm{~ms}^{-2}$]