A small wooden ball of density $ \rho$ is immersed in water of density $\sigma $ to depth $h $ and then released. The height $H$ above the surface of water up to which the ball will jump out of water is
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Net upward force acting on the body $F=\sigma V g-\rho V g$
$\Rightarrow m a=\sigma V g-\rho V g$
$\Rightarrow(\rho V) a=V g(\sigma-\rho)$
$\Rightarrow a=g\left(\frac{\sigma}{\rho}-1\right)$
Velocity $v$ after height $h=\sqrt{2 g\left(\frac{\sigma}{\rho}-1\right) h}$
Conserving mechanical energy at max height h'above surface,
$m g h^{\prime}=\frac{1}{2} m\left(2 g\left(\frac{\sigma}{\rho}-1\right) h\right)$
$\Rightarrow h^{\prime}=\left(\frac{\sigma}{\rho}-1\right) h$
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