Question

A solid sphere of radius 20cm is subjected to a uniform pressure of ${10}^6$ $N{m}^{-2}$. If the bulk modulus is $1.7\times {10}^{11}$ $N{m}^{-2}$, the decrease in the volume of the solid is approximately equal to:

• A. 0.2 $c{m}^3$
• B. 0.3 $c{m}^3$
• C. 0.4 $c{m}^3$
• D. 0.5 $c{m}^3$

Answer 1

Answer: (A)

0.2 $c{m}^3$

The volume of the sphere is $\frac{4}{3}\pi r^3=\frac{4\times 22\times 0.008}{3\times 7}=0.0335$

The pressure applied is ${10}^{6}N{m}^{-2}$

The Bulk modulus is defined as $B=\frac{PV}{X}$ , where $X$ is change in volume.

$\Rightarrow X=\frac{PV}{B}=\frac{{10}^6\times 0.0335}{1.7\times {10}^{11}}=0.2c{m}^3$

Therefore option $A$ is correct.