Question

A rectangular block of mass m and area of cross-section a floats in a liquid of density . If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period t. Then:

Answer 1

Answer:

T∝1/√A

Explanation:

Let I be the length of block immersed in liquid as shown in the figure. When the block rs floating,

mg=Alpm

If the block is given vertical displacement y then the effective restoring force is

F= -Alpgy

Restoring force =-[Alρg]y.As this F is directed towards its equilibrium position of block, so if the block is left free, it will execute simple harmonic motion-

Spring factor:-Aρg

therefore, time period = T = 2π√m/apg

thats means T directly proportional to 1/√A