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(C) Let the body sink to a maximum depth $H$. At this depth,the final velocity of the body becomes $v = 0$.When the body enters the water,it experienc

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$\frac{h \rho'}{\rho - \rho'}$

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(C) Let the body sink to a maximum depth $H$. At this depth,the final velocity of the body becomes $v = 0$.When the body enters the water,it experiences an upward buoyant force $F_B = V \rho g$ and a downward gravitational force $F_g = V \rho' g$,where $V$ is the volume of the body.The net downward acceleration $a$ inside the water is given by $a = \frac{F_g - F_B}{m} = \frac{V \rho' g - V \rho g}{V \rho'} = g \left( \frac{\rho' - \rho}{\rho'} \right) = -g \left( \frac{\rho - \rho'}{\rho'} \right)$.Using the kinematic equation $v^2 = u^2 + 2as$,where $u^2 = 2gh$ is the velocity just before entering the water,$v = 0$,and $s = H$:$0 = 2gh + 2 \left[ -g \left( \frac{\rho - \rho'}{\rho'} \right) \right] H$.Solving for $H$: $2gH \left( \frac{\rho - \rho'}{\rho'} \right) = 2gh$.$H = \frac{h \rho'}{\rho - \rho'}$.

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

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