Question

A ball of uniform density which is 2/3 of that of water is dropped freely into a pond from a height 10 m above its surface. The maximum depth the ball can travel in water is

• A. 21 m
• B. 10 m
• C. 20 m
• D. 30 m

Answer 1

The correct option is C 20 m

From third equation of motion, we can calculate the velocity with which the ball falls on the pond surface is
$v^2-u{}^2=2as$
$v^2=2\times 10\times 10$
$v^2=200$
$v=10\sqrt{2}m/s$
Let density of the water = d
upward thrust = Vdg
$=\frac{m}{D}dg$

$=\frac{m}{\frac{2d}{3}}dg$
$=\frac{3}{2}mg$


Net force acting on the ball
$F_{net}=F_{upward}-F_G$
$F_{net}=\frac{3}{2}mg-mg$
$F_{net}=\frac{1}{2}mg\left(upward\right)$
So, retarding force of $\frac{mg}{2}is$
acting on the ball
$a=-\frac{g}{2}$
$v{}^2-u^2=2as$
$-200=\text{/}2\times \frac{g}{\text{/}2}h$
200 = 10h
$h=20m$
$\text{maximum depth}\Rightarrow h=20m$