Question

What will be the magnitude and the direction of acceleration of the stone when a stone tied to the end of a string $80cm$ long is whirled in a horizontal circle with a constant speed and if the stone makes $14$ revolutions in $25s$?

Answer 1

Length of string, $l=80cm=80\times {10}^{-2}m$

Stone makes $14$ revolutions in $25$ second

$\therefore$ it makes $1$ revolution in $\frac{25}{14}s$

$\therefore$ time period $T=\frac{25}{14}s$

$\therefore$ angular speed $w=\frac{2\pi }{T}=\frac{2\pi }{25}\times 14=\frac{28\pi }{25}$

$\therefore$ centripetal force $=a_c=l{w}^2=80\times {10}^{-2}\times \frac{{\left(28\right)}^2{\pi }^2}{625}=9.9m/s^2$

Its direction is towards the center along the radius.