Question

A particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^2{R}^2{t}^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it is:

• A. $M$ $n$ $R^2$ $t^2$
• B. $M$ $n$ $R^2$ $t$
• C. $\frac{1}{2}$ $M$ $n^2$ $R^2$ $t^2$
• D. $M$ $n^2$ $R^3$ $t$

Answer 1

The correct option is D $M$ $n^2$ $R^3$ $t$

$As\frac{v^2}{r}=n^2{r}^2{t}^2\therefore v^2{=n}^2{r}^3{t}^{2}differentiatebothsideswrt{}^{\prime }{t}^{\prime }2v\frac{dv}{dt}=n^2{r}^3\times 2tor2va={2n}^2{r}^{3}twherea=\frac{dv}{dt}=accelerationnowPower=FV=MaV=M{n}^2{r}^{3}t$