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MHT CET 2024 (11 May, Shift 2) · Other SHM Systems

Other SHM Systems question from MHT CET 2024 (11 May, Shift 2)

Q11MHT CET 2024 · 11 MAY · SHIFT 2Medium

Other SHM Systems

A piece of wood has length, breadth and height, ' $a$ ', ' $b$ ' and ' $c$ ' respectively. Its relative density, is ' $d$ '. It is floating in water such that the side ' $a$ ' is vertical. It is pushed down a little and released. The time period of S.H.M. executed by it is ( $g =$ acceleration due to gravity)

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Answer: (d)

Horizontal face area $bc$ , mass $m = d\rho_w abc$ ; restoring constant $= \rho_w (bc) g$ .
$T = 2\pi\sqrt{\frac{d\rho_w abc}{\rho_w bc\, g}} = 2\pi\sqrt{\frac{ad}{g}}$ , answer (d).

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