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

Answer 1

Answer: (D)

$T \propto \frac{1}{\rho}$

Answer 2

Time period of SHM of small vertical oscillations in a liquid is given
by $T =2 \pi \sqrt{\frac{1}{ g }}$, where 1 is the length of
cube/cylinder/block dipped in the liquid. So according to law of floatation, weight of the block = weight of the liquid displaced $m g = A l p g$
$\Rightarrow 1=\frac{m}{A p}$
$\Rightarrow T =2 \pi \sqrt{\frac{ m }{ Apg }}$
So options A.C and D are true.