Question

A ball is dropped into water from a height of 9 cm. The density of ball is $0.4\times {10}^{3}kg/m^3$, then, to what depth does the ball sink?

• A. $3cm$
• B. $9cm$
• C. $6cm$
• D. $12cm$

Answer 1

The correct option is C $6cm$

Using equation
$v^2=u^2-2as$
We have $u=0,s=9cm$
$v=\sqrt{2g9}=\sqrt{18g}$
When, ball enters into water, due to upthrust of water the velocity of ball decreases.
Retardation a $=\frac{apparentweight}{massofbalk}$
$=\frac{V(\rho -\sigma )g}{Vp}$
$=\left(\frac{\rho -\sigma }{\rho }\right)g$
$=\left(\frac{0.4-1}{0.4}\right)\times g$
$=-\frac{3}{2}g$
Let h be depth upto which ball sinks, then
$0-v^2=2\times (-\frac{3}{2}g)\times h=3gh$
$\Rightarrow h=6cm$