Question

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 :

• A. T \(\propto\) \(\sqrt \rho\)
• B. T \(\propto\) \(\bigg(\frac{1}{\sqrt A}\bigg)\)
• C. T \(\propto\bigg(\frac{1}{\rho}\bigg)\)
• D. T \(\propto\bigg(\frac{1}{\sqrt m}\bigg)\)

Answer 1

The Correct Option is B

Time period of SHM is given by
T= \(2\pi\frac{\sqrt I}{g}\)
according to law of floatation
weight of the block = weight of the liquid displaced

mg=Al\(\rho\)\(g\)

l= \(\frac{m}{A\rho}\)

Then, T=\(2\pi\frac{\sqrt m}{A\rho g}\)

Now we can say that-

T \(\propto\) \(\bigg(\frac{1}{\sqrt A}\bigg)\)

Therefore, the correct option is (B): T \(\propto\) \(\bigg(\frac{1}{\sqrt A}\bigg)\)