An aluminum ball is subjected to a pressure of 7.00 × 106 Pa. The volume strain is −1.0 × 10−4. What is the bulk modulus?

The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

The formula for bulk modulus (K) is:

K = -P / ΔV/V

where:

• P is the pressure change,
• ΔV is the change in volume,
• V is the original volume.

Given in the problem:

• P = 7.00 × 10^6 Pa (pressure change)
• ΔV/V = -1.0 × 10^-4 (volume strain)

Substitute these values into the formula:

K = - (7.00 × 10^6 Pa) / (-1.0 × 10^-4)

Solving this gives:

K = 7.00 × 10^10 Pa

So, the bulk modulus of the aluminum ball is 7.00 × 10^10 Pa.