Question

A spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is

• A. $1 \times 10^{11} N / m ^{2}$
• B. $2 \times 10^{10} N / m ^{2}$
• C. $2.5 \times 10^{10} N / m ^{2}$
• D. $1 \times 10^{13} N / m ^{2}$

Answer 1

Answer: (C)

$\frac{\Delta v}{v}=-\frac{P}{B}$
$\left\{ \frac{\Delta v}{v} = \frac{-0.02}{100} \right\}$
$P=50\, atm =50 \times 1.01 \times 10^{5} Pa$ or $ N / m ^{2} $
So $ B =50 \times 1.01 \times 10^{5} \times \frac{100}{0.02} $
$ =2.5 \times 10^{10} N / m ^{2}$