Question

A boy whirls a stone in a horizontal circle of radius $1.5$ $\text{m}$ and at a height $2.0$ $\text{m}$ above level ground. The string breaks and the stone flies off tangentially and strikes the ground after travelling a horizontal distance of $10$ $\text{m}$. What is the magnitude of centripetal acceleration of stone while in motion?

• A. $64$ ${\text{m/s}}^2$
• B. $163$ ${\text{m/s}}^2$
• C. $15.63$ ${\text{m/s}}^2$
• D. $12$ ${\text{m/s}}^2$

Answer 1

The correct option is B $163$ ${\text{m/s}}^2$


Let the speed of the stone be $v$ when the string breaks. Time of flight for stone is given by :

$T$ =$\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\times 2}{9.8}}=0.64$ $\text{sec}$

Kinematic equation in horizontal direction,

$d=v\times T\Rightarrow 10=v\times 0.6$ ( $a_x$ $=$ $0$ )

$v$ $=$ $\frac{10}{0.64}$ $=$ $15.62$ $\text{m/s}$

Thus, centripetal acceleration of stone during circular motion is

$a_c=\frac{v^2}{R}=162.7=163$ ${\text{m/s}}^2$