Question

A spherical ball contracts in volume by $0.02\%$ when subjected to a normal uniform pressure of $100\text{atm}$. The bulk modulus of its material is

• A. $2.02\times {10}^{10}{\text{N/m}}^2$
• B. $1.01\times {10}^{11}{\text{N/m}}^2$
• C. $5.05\times {10}^{10}{\text{N/m}}^2$
• D. $1.01\times {10}^{10}{\text{N/m}}^2$

Answer 1

The correct option is C $5.05\times {10}^{10}{\text{N/m}}^2$

We know, Bulk modulus , $K=\frac{P\times V}{-\Delta V}$
where, negative sign indicates decrease in the volume of the ball.
$P=$ Pressure
$V=$ Original volume of spherical ball
$\Delta V=$ Change in the volume of spherical ball.
$K=\frac{100\times 1.01\times {10}^5\times V}{\frac{0.02\times V}{100}}=5.05\times {10}^{10}{\text{N/m}}^2$

$[\because 1\text{atm}=1.01\times {10}^5{\text{Pa or N/m}}^2]$

Option C is correct.