Question

A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 22 s, then the acceleration of the stone is:

• A. $16m{s}^{-2}$
• B. $4m{s}^{-2}$
• C. $12m{s}^{-2}$
• D. $8m{s}^{-2}$

Answer 1

The correct option is A $16m{s}^{-2}$

Here, r = 100 cm = 1 m
Frequency, $\upsilon =\frac{14}{22}Hz$
$\therefore \omega 2\pi \upsilon =2\times \frac{22}{7}\times \frac{14}{22}=4rad{s}^{-1}$
The acceleration of the stone is
$a_c={\omega }^{2}r=\left(4{)}^2\right(1)=16m{s}^{-2}$