question_answer

A wooden cube (density of wood ‘d’) of side \['\ell '\] floats in a liquid of density\['\rho '\] with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period T'. Then, T is equal to:                                                                                                                         [AIEEE 11-05-2011]

A) \[2\pi \sqrt{\frac{\ell d}{\rho g}}\]

B)                  \[2\pi \sqrt{\frac{\ell \rho }{dg}}\]

C) \[2\pi \sqrt{\frac{\ell d}{(\rho -d)g}}\]

D)      \[2\pi \sqrt{\frac{\ell \rho }{(\rho -d)g}}\]

Correct Answer: A

Solution :

[a]

At equilibrium

(i)

Restoring force,

.(i)