Question

A ball whose density is $5\times 10^{3}kg/m^3$ falls into the water from a height of $5m$. To what depth the ball will go?

• A. $7.8m$
• B. $5m$
• C. $6.25m$
• D. $9m$

Answer 1

Answer: (C)

Velocity of ball before entering into the water
$V=\sqrt{2gh}$
$=\sqrt{2\times 10\times 5}=10m/s$
Due to the upthrust the ball motion will retard.
upthrust $(F)=ma$
Apparent weight $=ma$
$\therefore \left(\frac{\rho -\sigma }{\rho }\right)g=a$
$\Rightarrow \left(\frac{5-1}{5}\right)\times 10=8m/s^2$
$v^2-u^2=2ah$
Due to upthrust after reaching its maximum depth final velocity becomes zero
$(0{)}^2-(V{)}^2=2as$
$-100=2\times 8\times h$
$\frac{-100}{16}=h$
$h=-6.25m($ -ve indicates depth $)$