Question

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

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

Answer 1

The correct option is A

$0.2c{m}^3$

Given, radius of the sphere, r = 20 cm = 0.2 m
Volume of sphere, $V=\frac{4\pi r^3}{3}$
Now, decrease in volume, $\Delta V=\frac{V\Delta P}{B}=\frac{4\pi }{3}\times \frac{(0.2{)}^3\times {10}^6}{1.7\times {10}^{11}}$
$\simeq 0.2\times {10}^{-6}{m}^3=0.2c{m}^3$
Hence, the correct choice is (a).