Ball Fall

Classical Mechanics Level 3

A ball of density $\rho$ is dropped from rest at a height $H$ into a lake of water with density $\sigma$ such that $\sigma > \rho$ . Neglecting damping forces, calculate the maximum depth to which the body sinks before turning around.

Assumptions

$H\gg r_{\rm{ball}}$ , i.e. the ball has some infinitesimal volume $dV$ .

\frac { H\times (\sigma -\rho ) }{ \sigma }

\frac { H\times (\rho -\sigma ) }{ \sigma }

\frac { H\times \rho }{ \rho -\sigma }

\frac { H\times \rho }{ \sigma -\rho }