1.

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 with a time period T, then

Answer»

`T prop 1/sqrt(m)`
`T prop sqrt(rho)`
`T prop 1/sqrt(A)`
`T prop 1/rho`

Solution :LET l be the length fo BLOCK immersed in liquid as shown in the FIGURE.
When the blocks is floating.
`therefor mg = Al rho g`

If the block is GIVEN vertical displacement y then the effective RESTORING force is,
`F =-[A(l +y)rho g - mg)] =-[A(l + y)rhog -Alrhog] =-Alrho gy`
here inertia factor = mass of block =m
Spring factor `=A rho g`
`therefore` Time period `=T = 2pi sqrt(m/(A rho g))`
i.e. `T prop 1/sqrt(A)`


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