PYQ NEET- Mechanical Properties Of Solids L-1

Question: The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $p$, the fractional decrease in radius is#

A) $\frac{p}{B}$

B) $\frac{B}{3 p}$

C) $\frac{3 p}{B}$

D) $\frac{p}{3 B}$

Answer: $\frac{p}{3 B}$#

Sol:#

The object is spherical and the bulk modulus is represented by $B$. It is the ratio of normal stress to the volumetric strain.

Hence $B=\frac{F / A}{\Delta V / V} \Rightarrow \frac{\Delta V}{V}=\frac{p}{B}$

$$ \Rightarrow\left|\frac{\Delta V}{V}\right|=\frac{p}{B} $$

Here $p$ is applied pressure on the object and $\frac{\Delta V}{V}$ is volume strain Fractional decreases in volume $$ \Rightarrow \quad \frac{\Delta V}{V}=3 \frac{\Delta R}{R} \quad\left[\because V=\frac{4}{3} \pi R^3\right] $$

Volume of the sphere decreases due to the decrease in its radius. Hence $\frac{\Delta V}{V}=\frac{3 \Delta R}{R}=\frac{p}{B}$ $$ \Rightarrow \quad \frac{\Delta R}{R}=\frac{p}{3 B} $$