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 \(dV\).

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