Question

A particle is moving in a circular path of radius $50cm$ with an uniform speed, completing one revolution in $10s$. The magnitude of centripetal acceleration of the particle is

• A. $5{\pi }^{2}cm/s^2$
• B. $2{\pi }^{2}m/s^2$
• C. $2{\pi }^{2}cm/s^2$
• D. $5{\pi }^{2}m/s^2$

Answer 1

The correct option is C $2{\pi }^{2}cm/s^2$

Centripetal acceleration $a_c=r{\omega }^2[\because v=r\omega ]$
To find $\omega$:
$\omega =\frac{2\pi }{T}=\frac{2\pi }{10}=\frac{\pi }{5}rad/s$
$\therefore a_c=50\times {10}^{-2}\times \frac{{\pi }^2}{25}m/s^2=2{\pi }^{2}cm/s^2$