A small solid ball is dropped from a height above the free surfac… - Vidyadip

Question

A small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500\ kg/m^3$ and that of liquid is $1000\ kg/m^3$ If the ball comes momeritariiy at rest at $t = 2\ sec$ then initial height of the ball from surface of liquid was ..... $m$ (neglect viscosity)

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Answer

Velocity of ball when it reaches to surface of liquid

$\mathrm{a}=\frac{1000 \mathrm{gV}-500 \mathrm{gV}}{500 \mathrm{V}}$

where $V$ is the volume of the ball.

$a=10 \mathrm{m} / \mathrm{sec}^{2}$

apply $\mathrm{v}=\mathrm{u}+\mathrm{at}$

$\Rightarrow 0=\sqrt{2 g h}-10 t$

$\Rightarrow \sqrt{2 g h}=10 \times(2)$

$\Rightarrow 2 \times 10 \times h=400$

$\Rightarrow \mathrm{h}=20\, \mathrm{m}$ Ans

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