The normal density of a material is ρ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

Solution

Physics sir · 3 steps

Mass stays fixed, so density goes up exactly as much as volume goes down. Use K to find that fraction.

1. Volume shrinks. Bulk modulus is K = P/(Δ V / V), so the fractional decrease in volume is (Δ V)/V = P/K.
2. Density rises. The mass m does not change, so ρ = m/V. For a small change, the fractional increase in density equals the fractional decrease in volume.

   (Δ ρ)/ρ = (Δ V)/V = P/K

3. So. The increase in density is Δ ρ = (ρ P)/K, which is option (c).

The idea to keep. Density and volume are inversely linked at fixed mass, so their small fractional changes are equal in size. Bulk strain is always P/K.

Answer from the NTA final answer key. Solution by PrepWiser.