Class 11 NEET Physics Oscillations Questions

Let l be the length of block immersed in liquid as shown in the figure. When the block is floating,
∴mg=Alρm
If the block is given vertical displacement y then the effective restoring force is
F=−[A(l+y)ρg−mg] =−[A(l+y)ρg−Alρg]
=−Alρgy
Restoring force =−[Alρg]y. As this F is directed towards equilibrium position of block, so if the block is left free, it will execute simple harmonic motion.
Here inertia factor = mass of block =m
Spring factor =Aρg
∴ Time period, T=2π√

m

Aρg

i.e., T∝

1

√A