Question

A stone tied to the end of a strings of $1m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44s$ what is the magnitude and direction of acceleration of the stone?

Answer 1

Given, Length of string $=1m$

Stone makes $22$ revolutions in $44sec$.

Hence, stone makes $\frac{22}{44}$ revolution in $1sec$

so frequency $=\frac{22}{44}se{c}^{-1}=\frac{1}{2}Hz$

We know, Angular speed $\omega =2\pi \times frequency$

$w=2\pi \times \frac{1}{2}=\pi rad/sec$

Now, acceleration $a={\omega }^{2}r$

where r is the radius {length of string}

Acceleration$=1\times {\pi }^2=9.8596m/s^2$