Question

A particle moves in a circle of radius 25 cm at two revolutions per sec. The acceleration of the particle in $m/s^2$ is :

• A. $\pi$
• B. $8{\pi }^2$
• C. $4{\pi }^2$
• D. $2{\pi }^2$

Answer 1

The correct option is C $4{\pi }^2$

Given :
$r=25\times {10}^{-2}m$
f = 2 revolutions/sec
$\omega =2\pi f=4\pi \text{rad/sec}$
Acceleration
$a=\frac{v^2}{r}=\frac{(\omega r{)}^2}{r}$
$={\omega }^{2}r=(4\pi {)}^2\times 25\times {10}^{-2}$
$=16\times 25\times {10}^{-2}{\pi }^{2}m/s^2$
$=4{\pi }^{2}m/s^2$