MHTCET 16 Apr 2026 Shift 1 Paper

Concept:When a floating body is displaced vertically, the change in buoyant force provides a restoring force, leading to simple harmonic motion (SHM).Explanation:In equilibrium, the weight of the block is balanced by the buoyant force. Let the block be pushed down by a small distance $x$. The extra volume of liquid displaced is $A x$. The additional upward buoyant force is $\varrho g A x$. This force opposes the displacement, so the restoring force is $F = -\varrho g A x$. Using Newton's second law, $m \frac{d^{2}x}{dt^{2}} = -\varrho g A x$. Rearranging, $\frac{d^{2}x}{dt^{2}} + \frac{\varrho g A}{m}x = 0$. This is the standard SHM equation, giving $\omega^{2} = \frac{\varrho g A}{m}$. So $\omega = \sqrt{\frac{\varrho g A}{m}}$. The frequency is $f = \frac{\omega}{2\pi} = \frac{1}{2\pi}\sqrt{\frac{A \varrho g}{m}}$.Answer:$f = \frac{1}{2\pi}\sqrt{\frac{A \varrho g}{m}}$, which is Option C.