Question

A particle of mass m is moving in a circular path of constant radius 'r' such that its centripetal acceleration $a_c$ is proportional to $t^n$ (where 't' is time ). Then the power 'p' is proportional to

• A. $t^n$
• B. $t^{n-2}$
• C. $t^{n-1}$
• D. None of these

Answer 1

The correct option is C $t^{n-1}$

$a_c\alpha t^n$

$\Rightarrow \frac{m{v}^2}{r}\alpha t^n$

$\Rightarrow v^2\alpha t^n$

$\Rightarrow k\alpha t^n$

$\Rightarrow \frac{dk}{dt}\alpha t^{n-1}$

$\therefore p\alpha t^{n-1}$

Hence,

option $\left(C\right)$ is correct answer.