A spherical steel ball with a bulk modulus of 160 GPa is subjected to a uniform external pressure of 40 MPa. What is the volumetric strain experienced by the steel ball?  

Explanation:

Volumetric Strain in a Spherical Steel Ball

Definition: Volumetric strain is defined as the change in volume divided by the original volume of a material when subjected to stress. It is a measure of the deformation experienced by the material due to an applied pressure.

Formula for Volumetric Strain:

The volumetric strain (ε_v) is given by the formula:

ε_v = -P / K

Here,

• ε_v = Volumetric strain
• P = External pressure applied
• K = Bulk modulus of the material

The negative sign indicates that the volume decreases under pressure.

Calculation:

Given Data:

• Bulk modulus (K) of steel = 160 GPa = 160 × 109 Pa
• External pressure (P) = 40 MPa = 40 × 106 Pa

Substituting the given values into the formula:

ε_v = - (40 × 10⁶ Pa) / (160 × 10⁹ Pa)

ε_v = - (40 / 160) × 10^-3

ε_v = - (1 / 4) × 10^-3

ε_v = - 0.25 × 10^-3

ε_v = - 2.5 × 10^-4

Interpreting the Result:

The volumetric strain experienced by the steel ball is -2.5 × 10^-4. The negative sign denotes a reduction in volume due to the applied pressure.