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 $n^{2}R{t}^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it, is:

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

Answer 1

The correct option is B $M{n}^2{R}^{2}t$

$a_c=\frac{V^2}{R}=n^{2}R{t}^2$

$⟹V=nRt$

$a_t=\frac{dv}{dt}=nR$

$Power=m{a}_{t}v$

$=mnR\times nRt$

$=M{n}^2{R}^{2}t$