Question

A small body density ${\rho }^{\prime }$ is droop from at a height $h$ into a lake of density $\rho$, where $\rho >{\rho }^{\prime }$ . Which of the following statement is/are correct if all dissipative effect are neglect (neglect viscosity)?

• A. The speed of the body just entering the lake is $\sqrt{2gh}$.
• B. The body in the lake experiences upward acceleration equal to $\left\{\right(\rho /{\rho }^{\prime })-1\}g$.
• C. The maximum depth to which the body sinks in the lake is $h{\rho }^{\prime }/(\rho -{\rho }^{\prime })$.
• D. The body does not come back to the surface of the lake.

Answer 1

The correct option is C The maximum depth to which the body sinks in the lake is $h{\rho }^{\prime }/(\rho -{\rho }^{\prime })$.

Work done by gravity $=$ changein K.E

$mgh=\frac{1}{2}m{v}^2\Rightarrow v=\sqrt{2gh}$

Inside water:

Upward acceleration of block $=\frac{\rho Vg-{\rho }^{1}Vg}{{\rho }^{1}g}=(\frac{\rho }{{\rho }^1}-1)g$

For maximum depth-

$v^2=u^2+2as(0{)}^2=(\sqrt{2gh}{)}^2+2(\frac{\rho }{{\rho }^1}-1)g(-s)-2gh=-2gs\left(\frac{\rho -rh{o}^1}{{\rho }^1}\right)\frac{{\rho }^{1}h}{\rho -{\rho }^1}=s$