Question

A ball of relative density $0.8$ fall into water from a height of $2$m. The depth to which the ball will sink is

• A. $8m$
• B. $2m$
• C. $6m$
• D. $4m$

Answer 1

The correct option is A

$8m$

Step 1

Velocity of the ball as it reaches water surface is

$\sqrt{2gh}$ i.e. $\sqrt{4g}$

Let's say, $\rho$ is the density of ball and $\sigma$is the density of water. Now

Net upward force acting on the body F = $\sigma$V g – $\rho$V g

$$\begin{gathered} ma=\sigma Vg–\rho Vg \\ (\rho V)a=Vg(\sigma –\rho ) \\ a=g(\frac{\sigma }{\rho }–1)=g(\frac{1}{0.8}–1) \\ a=\frac{g}{4}inupwarddirection \end{gathered}$$

Step 2

Let's say it sink to the depth $H$, at this, instant final velocity becomes $V=O$.

So, we have,

$$\begin{gathered} V^2=u^2+2as \\ 0={(\sqrt{4g})}^2–2\times \frac{g}{4}\times H \\ 4g=\frac{2gH}{4} \\ H=8m \end{gathered}$$

Hence, correct option is (a).