Question

A body of density $\rho$ enters a tank of water of density ${\rho }^{\prime }$ after falling through a height h. The maximum depth to which it sinks in water is?

• A. $\frac{h{\rho }^{\prime }}{(\rho -{\rho }^{\prime })}$
• B. $\frac{h\rho }{(\rho -{\rho }^{\prime })}$
• C. $\frac{h\rho }{{\rho }^{\prime }}$
• D. $\frac{h{\rho }^{\prime }}{\rho }$

Answer 1

The correct option is A $\frac{h{\rho }^{\prime }}{(\rho -{\rho }^{\prime })}$

Initial velocity on entering water is $u=\sqrt{2gh}$.
Effective retardation in water is $g_{eff}=\frac{g(\rho -{\rho }^{\prime })}{{\rho }^{\prime }}$.
For maximum depth, final velocity $v=0$. If s is the maximum depth, then we have, from $v^2-u^2=2g_{eff}s$,
$0-2gh=-\frac{2g(\rho -{\rho }^{\prime })}{{\rho }^{\prime }}$ or $s=\frac{h{\rho }^{\prime }}{(\rho -{\rho }^{\prime })}$.