Question

A cylindrical block of the density `rho` is partically immersed in a liwuid of density `3rho`. The plane surface of the block remains parallel to the surface of the liquid. The height of the block is `60 m`. The block perform `SHM` when displaced form its mean position [Use `g = 9.8 m//s^(2)`]
A. the maximum amplitude is `20 cm`.
B. the maximum amplitude is `40 cm`
C. the time period will be `2pi//7` seconds
D. none

Answer 1

Correct Answer - A::C
When cylindrical block is partially immersed
`F_(B) = mg rArr 3rhoAyg = rhoA(60 xx 10^(-2)) g`
`y = 20 cm`
`rArr` Maximum amplitude `= 20 cm`

Restoring force when it is slightly depressed by an amount of `x`.
`F = - (DeltaVsigmag) = - (Asigmag)x`
`T = 2pisqrt((m)/(Asigmag)) = 2pisqrt((rhoAh)/(A3rhog)) = 2pisqrt((h)/(3g))`
`= 2pisqrt((60 xx 10^(-2))/(3 xx 9.8)) = (2pi)/(7)s`