Question

The density of the liquid varies as ρ = ρ∘y^3 the pressure at the depht of h is

Answer 1

ρ=2ρo(a+βh)

V=ρom

Downward force, F=mg−ρom2ρo(a+βh)g

F=mg((1−2a)−2βh)

So F is proportional to displacement from center position which is mg(1−2a) below surface

Therefore, the motion is SHM.

A = mg(1−2a)

k=2mgβ

Also, k=mω2

=> ω=2gβ

vmax=ωA=2β(2−a)g

Answer A

hope it helps uu