Question

A body of density '$\rho$' is dropped from rest at a height h into a lake of density $\rho$ where $\rho >{\rho }^{\prime }$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

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

Answer 1

The correct option is D $\frac{h\rho }{\rho -{\rho }^{\prime }}$

The effective acceleration of the body $g^{\prime }=(1-\frac{{\rho }^{\prime }}{\rho })g$
The depth to which the body sinks: $h^{\prime }=\frac{v^2}{2g^{\prime }}=\frac{2gh}{2g^{\prime }}=\frac{gh}{g^{\prime }}=\frac{gh}{(1-\frac{{\rho }^{\prime }}{\rho })g}=\frac{\rho h}{\rho -{\rho }^{\prime }}$