Question

A body of density $\rho$ is dropped from rest from a height h into a lake of density $\sigma$, where $\sigma >\rho$. Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface

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

Answer 1

The correct option is C $\frac{h\rho }{\sigma -\rho }$

${V_f}^2-V_1^2=2as$

$\Rightarrow r-\left(2gh\right)=2\times -(\frac{\sigma }{\delta }-1)g\times s$

$\Rightarrow s=\left(\frac{h}{\frac{\sigma }{\delta }-1}\right)$

$\Rightarrow [s=\frac{h\rho }{\sigma -\rho }]$