Question

A particle moving in a circle of radius $50$ cm with a uniform speed completes a revolution in $40$ s. The magnitude of the centripetal acceleration it experiences is ____ $cm{s}^{-2}$:

• A. $3.2{\pi }^2$
• B. $6.3{\pi }^2$
• C. $10.2{\pi }^2$
• D. $0.13{\pi }^2$

Answer 1

The correct option is D $0.13{\pi }^2$

Radius, $r=50$ $cm$

Time period, $T=40$ $s=\frac{2\pi r}{v}$

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

$\Rightarrow v=\frac{2\pi \times 50}{40}$

$\Rightarrow v=2.5\pi$ $cm/s$

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

$\Rightarrow a=\frac{6.25{\pi }^2}{50}$

$\Rightarrow a=0.125{\pi }^2$ $cm/s^2$

$\Rightarrow a\approx 0.13{\pi }^2$ $cm/s^2$