A wooden cube

Question:

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 :-

  1. $2 \pi \sqrt{\frac{\ell \rho}{(\rho-\mathrm{d}) g}}$

  2. $2 \pi \sqrt{\frac{\ell \mathrm{d}}{\rho \mathrm{g}}}$

  3. $2 \pi \sqrt{\frac{\ell \rho}{d g}}$

  4. $2 \pi \sqrt{\frac{\ell \mathrm{d}}{(\rho-\mathrm{d}) g}}$

Correct Option: , 2

Solution:

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