Question

A particle of mass $0.1\text{kg}$ is moving in a circular path of radius, $r=0.2\text{m}$ such that centripetal acceleration is varying with time $t$ as $100r{t}^2$. The power delivered to the particle by the force acting on it at $t=10\text{sec}$ is,

• A. $1\text{W}$
• B. $4\text{W}$
• C. $5\text{W}$
• D. $10\text{W}$

Answer 1

The correct option is B $4\text{W}$

Given that,

Centripetal acceleration, $a_c=100r{t}^2$

As, $a_c=\frac{v^2}{r}$

$\Rightarrow \frac{v^2}{r}=100r{t}^2$

$\Rightarrow v=10rt....\left(1\right)$

The work done by the centripetal force is zero because the direction of centripetal force is perpendicular to the velocity.

Tangential acceleration of the particle,

$a_t=\frac{dv}{dt}=10r.....\left(2\right)$

Tangential force acting on the particle,

$F=m{a}_t=10mr$

The power delivered to the particle is,

$P=\overrightarrow{F}.\overrightarrow{v}=Fv\cos \theta$

$\therefore P=Fv=\left(10mr\right)\times 10rt(\because \theta =0^{\circ })$

$\Rightarrow P=100m{r}^{2}t$

Substituting the values,

$\Rightarrow P=100\times 0.1\times {0.2}^2\times 10=4\text{W}$

Hence, option (b) is the correct answer.