Question

When the pressure on a sphere is increasedby 80 atmospheres , its volume decreases by 0.01%. Find the bulk modulus of elasticity of the material of the sphere ?

Answer 1

Answer on Question#38131 – Physics - Mechanics

When the pressure on a sphere is increased by 80 atmospheres, its volume decreases by 0.01%. Find the bulk modulus of elasticity of the material of the sphere?

Solution:

Here, increase in pressure, $p = 80$ atmosphere. Now, 1 atmosphere = $1.013 \times 10^{5} \frac{\mathrm{N}}{\mathrm{m}^{2}} \Rightarrow p = 80 \cdot 1.013 \times 10^{5} \frac{\mathrm{N}}{\mathrm{m}^{2}}$ and $\frac{\Delta V}{V} = \frac{0.01}{100}$.

Bulk modulus:

$$B = \frac{p}{\left(\frac{\Delta V}{V}\right)} = \frac{80 \cdot 1.013 \times 10^{5} \frac{\mathrm{N}}{\mathrm{m}^{2}}}{\left(\frac{0.01}{100}\right)} = 8.1 \cdot 10^{10} \frac{\mathrm{N}}{\mathrm{m}^{2}}.$$

Answer: Bulk modulus is equal to $8.1 \cdot 10^{10} \frac{\mathrm{N}}{\mathrm{m}^{2}}$.