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Q.

A wooden cube (density of wood ‘d’) of side ‘l ’ floats in a liquid of density ‘ρ ’ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period ‘T’

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a

2πldρg

b

2πlρdg

c

2πld(ρ−d)g

d

2πlρ(ρ−d)g

answer is A.

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Detailed Solution

At equilibrium  Fb=mg ρAl0g=dAlgRestoring force,F=mg- Fb'F=mg- ρA(l0+x)g dAla=dAlg−ρAl0g−ρgAxa=−ρgdlxTherefore, wooden cube performs S.H.M∴ω=ρgdl  ⇒T=2πldρg
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