Question

A body of density $\rho$ is dropped from rest from height $h$ (from the surface of water ) into a lake of density of water $\sigma (\sigma >\rho )$ .Neglecting all dissipative effects, the acceleration of body while it is in the lake is:

• A. $g(\frac{\sigma }{\rho }-1)$ upwards
• B. $g(\frac{\sigma }{\rho }-1)$ downwards
• C. $g\left(\frac{\sigma }{\rho }\right)$ upwards
• D. $g\left(\frac{\sigma }{\rho }\right)$ downwards

Answer 1

The correct option is A $g(\frac{\sigma }{\rho }-1)$ upwards

Velocity of the object as it reaches water surface is $\sqrt{2gh}$
Net upward force acting on the object $F=\rho Vg-\sigma Vg$
$\Rightarrow ma=\rho Vg-\sigma Vg$
$\Rightarrow \left(\sigma V\right)a=Vg(\rho -\sigma )$
$\Rightarrow a=g(\frac{\rho }{\sigma }-1)$ in upward direction