Question

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

• A. $146.7{\text{m/s}}^2$
• B. $166.7{\text{m/s}}^2$
• C. $156.7{\text{m/s}}^2$
• D. $176.7{\text{m/s}}^2$

Answer 1

The correct option is B $166.7{\text{m/s}}^2$


Motion along $x-$direction gives,
$v_{x}t=10..........\left(1\right)$

Motion along along $y-$direction,

$-2=0\times t-\frac{1}{2}\times 10\times t^2$

$\Rightarrow$$-2=-\frac{1}{2}\times 10\times t^2$

$\Rightarrow t=\sqrt{\frac{2}{5}}........\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$,

$v\times \sqrt{\frac{2}{5}}=10$

$\Rightarrow v=10\sqrt{\frac{5}{2}}.........\left(3\right)$

Now centripetal acceleration

$a_c=\frac{v^2}{r}$

$a_c=\frac{(10\sqrt{\frac{5}{2}}{)}^2}{r}$

$\Rightarrow a_c=\frac{100\times \frac{5}{2}}{1.5}\Rightarrow a_c=166.7{\text{m/s}}^2$

Why this question? This question is intended to test the understanding of circular motion and projectile motion. Concepts involved: 1. Projecticle motion. 2. Circular motion.