Question

A boy whirls a stone in a horizontal circle at a height of $31.25\text{m}$ above ground level and radius of circle being $3\text{m}$. Somehow, the string breaks and stone flies off horizontally and strikes the ground after travelling horizontal distance of $5\text{m}$. Find the magnitude of centripetal acceleration of stone while being in circular motion. Assume stone to be in uniform circular motion.

• A. $1.75{\text{m/s}}^2$
• B. $6.6{\text{m/s}}^2$
• C. $1.3{\text{m/s}}^2$
• D. $2.6{\text{m/s}}^2$

Answer 1

The correct option is C $1.3{\text{m/s}}^2$

The motion scenario of stone has been depicted in figure given below as the top view.

The path of stone will be that of a horizontal projectile, after the string breaks.

$h=31.25\text{m},x=5\text{m},r=3\text{m}$
$\text{Time of flight for stone(T)}=\sqrt{\frac{2h}{g}}\therefore T=\sqrt{\frac{62.5}{10}}=2.5\text{s}$
$\Rightarrow \text{Range}=u_x\times T$, let $u_x=v$
$\therefore x=v\times 2.5$
or, $5=2.5v$
or, $v=2\text{m/s}$

$\therefore a_c=\frac{v^2}{r}=\frac{4}{3}{a}_c=1.3{\text{m/s}}^2$