Question

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

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

Answer 1

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

Angular velocity of particle $\omega =2\times 2\pi$
$=4\pi rad/s$

Since angular velocity is constant, there is no tangential acceleration.
Centripetal acceleration $a_c$ is given by
$a_c={\omega }^{2}r=(4\pi {)}^2\times 0.25$
$=4{\pi }^2$

Therefore net acceleration $=a_c=4{\pi }^{2}m/s^2$