Question

A ball whose density is $0.4\times {10}^{3}kg/m^3$ falls into water from a height of $9cm$. To what depth does the ball sink?

• A. $9cm$
• B. $6cm$
• C. $4.5cm$
• D. $2.25cm$

Answer 1

Answer: (B)

$6cm$

The velocity of ball before entering the water surface
$v=\overline{2gh}=\underset{9}{\overline{2g}X}$
When ball enters into water, due to upthrust of water, the velocity of ball decreases (or retarded)
The retardationm
$a=\frac{apparentweight}{massofball}$
$=\frac{v(\rho -\sigma )g}{V\rho }=\frac{(\rho -\sigma }{=}\frac{(\rho -\sigma )g}{\rho }$
$=\left(\frac{(0.4-1)}{0.4}\right)g=-\overline{2}g$
If $h$ be the depth upto which ball $\sin x$, then
$0-v^2=2\times h\left(\frac{-3}{2}g\right)X$
$\Rightarrow 2g\times 9=3gh\therefore h=6cm$.