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

Options

A. `Tpropsqrt(rho)`
B. `Tprop(1)/(sqrt(A))`
C. `Tprop(1)/(sqrt(rho))`
D. `Tprop(1)/(sqrt(m))`

Answer

b

Explanation

Let block is displaced through x m, then weight of displaced water or upthrust (upwards)
`+-Axrhog`
Where, A is area of a cross-section of the block and r is
density. This must be equal to force (= ma) applied wherem
is mass of the block and a is acceleration.
`thereforema=-Axrhog`
or `a=-(Arhog)/(m)x=-omega^(2)x`
This is equation of SHM .
The time period of oscillation ,
`T=(2pi)/(omega)=2pisqrt((m)/(Arhog))`
`rArrTprop(1)/(sqrt(A))`