Question

A boy whirls a stone of small mass in a horizontal circle of radius $1.5$ m and at height $2.9$ m above level ground. The string breaks and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of $10$ m. What is the magnitude of the centripetal acceleration of the stone while in circular motion?

• A. $33m{s}^{-2}$
• B. $63m{s}^{-2}$
• C. $93m{s}^{-2}$
• D. $113m{s}^{-2}$

Answer 1

The correct option is D $113m{s}^{-2}$

Given : $r=1.5$ m $OA=h=2.9$ m $OB=10$ m

The string breaks at point A, from there onwards the stone follows a projectile motion as if it is thrown horizontally with a velocity $v$ from a height $h$ such that OB is the range of the projectile motion.

Time of flight $T=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 2.9}{9.8}}=0.77$ s

Using $OB=vT$

$\therefore$ $10=v\times 0.77$ $⟹v=13m/s$

Radial acceleration $a_r=\frac{v^2}{r}=\frac{{13}^2}{1.5}=113$ $m/s^2$