Question

A juggler keeps $n$ balls going with one hand, so that at any instant, $(n-1)$ balls are in air and one ball in the hand. If each ball rises to a height of $x$ metres, the time for each ball to stay in his hand is

• A. $\frac{1}{n-1}\sqrt{\frac{2x}{g}}$
• B. $\frac{2}{n-1}\sqrt{\frac{2x}{g}}$
• C. $\frac{2}{n}\sqrt{\frac{2x}{g}}$
• D. $\frac{1}{n}\sqrt{\frac{2x}{g}}$

Answer 1

Answer: (B)

Let $u$ be the initial velocity of the ball while going upwards. The final velocity of the ball at height $x$ is, $v=0$ .
So $u=\sqrt{2gx}$
Time of flight, $T=\frac{2u}{g}=\frac{2}{g}\sqrt{2gx}=2\sqrt{\frac{2x}{g}}$
During time $T$ , $(n-1)$ balls will be in air and one ball will be in hand. So time for one ball in hand
$=\frac{T}{\left(n-1\right)}=\frac{2\sqrt{2x/g}}{\left(n-1\right)}=\frac{2}{n-1}\sqrt{\frac{2x}{g}}$