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A wooden cube (density of wood 'd') of s...

A wooden cube (density of wood `'d'`) of side `'l'` flotes in a liquid of density `'rho'` with its upper and lower surfaces horizonta. If the cube is pushed slightly down and released, it performs simple harmonic motion of period `'T'`. Then, `'T'` is equal to :-

A

`2pisqrt(1p/(p-d)g)`

B

`2pisqrt(1p/pg)`

C

`2pisqrt(1p/dg)`

D

`2pisqrt(1p/(p-d)g)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let at any instant, cube be at a depth x from the equilibrium position, then
Net force acting on the cube = Upthrust on the portion of length x
`F=-pi^(2)xg=-pi^(2)gx` …..(i)
` Falpha-x(SHM)`
Negative sign shows that force is oppsite to x. Hence, equation of SHM
F=-kx
.....(ii)
Comparing Eqs.(i)and(ii),we get
`k=pi^(2)g`
`therefore T=2pisqrt(m/k)=2pisqrt((r^(3)d)/(pr^(2)g))=2pisqrt((1d)/(pg))`
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