Question

A ball of radius r and density $\rho$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is n, the value of h is given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Velocity of ball when it strikes the water surface $v=\sqrt{2gh}\cdots \left(i\right)$

Terminal velocity of ball inside the water $v=\frac{2}{9}{r}^{2}g\frac{\rho -1}{n}\cdots \left(ii\right)$

Equating (i) and (ii) we get $\sqrt{2gh}=\frac{2}{9}\frac{r^{2}g}{n}(\rho -1)$

$\Rightarrow h=\frac{2}{81}{r}^4{\left(\frac{\rho -1}{n}\right)}^{2}g$