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A plank of area of cross-section 'A' is half immersed in liquid 1 of density ‘ρ’ and half in liquid 2 of density 2ρ . The period of oscillation of the plank when it is slightly depressed downwards is

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$2 π \sqrt{\frac{m}{ρ Ag}}$

$π \sqrt{\frac{m}{ρ Ag}}$

$2 π \sqrt{\frac{3 m}{2 p A g}}$

$2 π \sqrt{\frac{m}{3 ρ Ag}}$

answer is A.

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Detailed Solution

The net buoyancy force acting on the block if it is given a downward displacement x is = −2xAg−(−xAg)=−Agx

Since buoyant force acts as restoring force, we can write ma=−Agx or a=−(Ag/m)x=− $ω^{2}$ x

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