Question

The bulk modulus of a material is 1.0 × 10¹¹ N/m². What fractional change in volume does a piece of this material undergo when it is subjected to a bulk stress increase of 10⁷ N/m²? Assume that the force is applied uniformly over the surface.

a) 0.01
b) 0.1
c) 0.001
d) 0.0001

Answer 1

The fractional change in volume of a material can be determined using the formula: ΔV/V = -ΔP/B, where ΔV represents the change in volume, V is the original volume, ΔP is the change in pressure (bulk stress), and B is the bulk modulus of the material. Substituting the given values into the formula, we find that the fractional change in volume is 0.0001.

Step-by-step explanation:

The fractional change in volume of a material can be determined using the formula:

ΔV/V = -ΔP/B

where ΔV represents the change in volume, V is the original volume, ΔP is the change in pressure (bulk stress), and B is the bulk modulus of the material.

Given that the bulk modulus is 1.0 × 10^11 N/m² and the bulk stress increase is 10^7 N/m², we can substitute the values into the formula to calculate the fractional change in volume:

ΔV/V = -(10^7 N/m²)/(1.0 × 10^11 N/m²)

Simplifying the expression gives us:

ΔV/V = -10^-4

Therefore, the fractional change in volume is 0.0001, which corresponds to option d) 0.0001.