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A rectangular block of mass m and area o...

A rectangular block of mass m and area of cross-section A floats in a liquid of density `rho`. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then

A

`T prop(1)/(rho)`

B

`T prop(1)/(sqrtm)`

C

`T prop sqrtrho`

D

`T prop (1)/(sqrtA)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, `mg=Al rho g`
If the block is given vertical displacement y then the effective restoring force
`F=-[A(l+y)rhog-mg]=-Arhogy`
For SHM, `Fprop-y`

`implies F= m a =-(A" "rho" "g)y`
`a=-((A" "rho" "g)/(m))y and a=-omega^(2)y`
`therefore omega=((A" "rho" "g)/(m))`
`therefore T=2pi sqrt((m)/(A" "rho" "g)) implies T prop (1)/(sqrtA)`
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