Question

A particle, moving in a circle of radius $10$ cm with a uniform speed, completes a revolution in $4$ seconds. The magnitude of the centripetal acceleration it experiences is ____ $cm{s}^{-2}$

• A. $2.5{\pi }^2$
• B. $5{\pi }^2$
• C. $3{\pi }^2$
• D. $6{\pi }^2$

Answer 1

The correct option is A $2.5{\pi }^2$

Radius, $r=10$ $cm$

Time period, $T=4$ $s=\frac{2\pi r}{v}$

$\Rightarrow v=\frac{2\pi r}{T}$

$\Rightarrow v=\frac{2\pi \times 10}{4}$

$\Rightarrow v=5\pi$ $cm/s$

Centripetal acceleration, $a=\frac{v^2}{r}$

$\Rightarrow a=\frac{2.5{\pi }^2}{10}$

$\Rightarrow a=2.5{\pi }^2$ $cm/s^2$