Question

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

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

Answer 1

The correct option is B

6 cm

Velocity of ball just before entering the surface of water $\sqrt{2gh}=\sqrt{2\times 10\times 9}cm/s$

This velocity retarded by upthrust acting on the ball due to waterRetardation

$=\frac{V\rho g-V\delta g}{V\rho }=\left[\frac{\rho -\delta }{\rho }\right]g=\left[\frac{0.4-1}{0.4}\right]g=-\frac{3}{2}g$
Depth of penetration of ball
$0^2-2\times 980\times 9=2[-\frac{3}{2}]\times 980hh=6cm$