Question

A metal ball of radius $1mm$ and density ${10}^4$kg m${}^{-3}$. falls freely in air through a height '$h$' before falling in a tank full of water. If on falling in water its velocity remains unchanged, then the value of h will be (Coefficient of viscosity of water $={10}^{-3}$ Pa.s and $g=10m{s}^{-2}$)

• A. $10m$
• B. $15m$
• C. $25m$
• D. $20m$

Answer 1

The correct option is D $20m$

As the velocity of the ball remains unchanged in the water which implies that the ball reached its terminal velocity in water,(just before touching the water)

$V=\frac{2r^2(T_s-T)g}{9\eta }=\frac{2\left({10}^{-3}\right)\times 10\times ({10}^4-{10}^3)}{9\times {10}^{-3}}=20m/s$
Neglecting the viscous effect of air,

We calculate the distance covered by the ball to reach the velocity of $20m/s$
$V^2-V^2=2aS$
$\Rightarrow (20{)}^2=2\times 10\times h$
$\Rightarrow \frac{400}{20}=h\Rightarrow h=20m.$