Final answer:
The material with a bulk modulus of 1.0 × 1011 N/m2 undergoes a fractional change in volume of -1.0 × 10-4 when subjected to a bulk stress increase of 107 N/m2.
Step-by-step explanation:
The bulk modulus (B) is defined as the ratio of the bulk stress to the bulk strain in a material. When a material undergoes a bulk stress, it experiences a change in volume, called bulk strain, which can be expressed as the fractional change in volume (ΔV/V0), where ΔV is the change in volume and V0 is the initial volume. The bulk modulus formula is given by B = -ΔP / (ΔV/V0), where ΔP is the increase in pressure (or bulk stress).
For the given material with a bulk modulus of 1.0 × 1011 N/m2, and a bulk stress increase of 107 N/m2, we can calculate the fractional change in volume as follows:
Substitute the known values into the bulk modulus equation:
B = -ΔP / (ΔV/V0)
(1.0 × 1011 N/m2) = -(107 N/m2) / (ΔV/V0)
Therefore, the fractional change in volume ΔV/V0 is:
ΔV/V0 = -(107 N/m2) / (1.0 × 1011 N/m2)
ΔV/V0 = -0.0001 or -1.0 × 10-4
The negative sign indicates a decrease in volume. Thus, the material undergoes a fractional volume change of -1.0 × 10-4.