A metal block of volume $0.05 m^{3}$ has a bulk modulus of $120 GPa$ . If a uniform external pressure of $4 MPa$ is applied, what is the fractional change in volume of the block?

easy 3 marks Class 11 · Physics · Mechanical Properties of Solids

Answer

-3.33×10⁻⁵

The correct answer is -3.33×10⁻⁵ — Thus the volume decreases by $3.33 \times 1 0^{- 5}$ fraction of its original value.

Step-by-step solution

Compute bulk modulus in SI units: $K = 120 GPa = 120 \times 1 0^{9} Pa$ .
Compute pressure in SI units: $Δ P = 4 MPa = 4 \times 1 0^{6} Pa$ .
Use the relation for bulk modulus: $\frac{Δ V}{V} = - \frac{Δ P}{K}$ .
Insert the values: $\frac{Δ V}{V} = - \frac{4 \times 1 0 ^{6}}{120 \times 1 0 ^{9}} = - 3.33 \times 1 0^{- 5}$ .
Thus the volume decreases by $3.33 \times 1 0^{- 5}$ fraction of its original value.

Common mistake: Using

K = - V D e l t a P / D e l t aV

instead of the correct sign convention

Concept tested: Bulk modulus and volumetric strain