A small metal sphere of density $\rho$ is dropped from height $h$ into a jar containing liquid of density $\sigma (\sigma > \rho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces)
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Work-Energy Theorem: $W_{net} = \Delta KE$. At max depth, $KE = 0$. $W_g + W_b = 0$.