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

The Correct Option is A

The correct option is(A): \(M \, n^2 R^2 t\)

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