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

Answer 1

Answer: (A)

$\frac{V^{2}}{R}=n^{2}\, R t^{2}$
$\Rightarrow V^{2}=n^{2}\, R^{2}\, t^{2}$
$\Rightarrow V=n R t$
$\Rightarrow \frac{d V}{d t}=n R$
$P=F_{t} V$
$=\frac{m d V}{d t} V$
$=m n R .n R t$
$P=n^{2}\, R^{2}\, t\, m$