Question

A boy whirls a sand stone in a horizontal circle $1.8$ m above the ground by means of a string with radius $1.2$ m. While whirling the stone string was horizontal, Suddenly the stone breaks and sand clusters fly off horizontally striking the ground $9.1$ m away. The centripetal acceleration during the circular motion was nearly: (use $g=9.8m{s}^{-2}$

• A. $94m/s^2$
• B. $141m/s^2$
• C. $188m/s^2$
• D. $282m/s^2$

Answer 1

Answer: (C)

$188m/s^2$

First we calculate the time it takes to reach the ground. (initial vertical velocity is 0).
$h=\frac{1}{2}g{t}^2$
we get $t=\sqrt{\frac{2h}{g}}=0.606s$
i.e. horizontal velocity $=\frac{9.1}{t}=15.014m{s}^{-1}$
Centripetal acceleration $=\frac{v^2}{R}=187.85m{s}^{-2}$
Option C is correct.