The increase in pressure required to decrease the volume of a water sample by 0.2 % is P × 10⁵ Nm⁻². Bulk modulus of water is 2.15 × 10⁹ Nm⁻². The value of P is _________ .

Solution

Physics sir · 4 steps

Bulk modulus is pressure per unit fractional volume change, so multiply B by the strain.

1. Definition. Bulk modulus is the extra pressure divided by the fractional decrease in volume. Rearranging gives the pressure needed for a given volume strain.

   Δ P = B × (Δ V)/V

2. Volume strain. A 0.2% decrease means (Δ V)/V = 0.2/100 = 2 × 10⁻³.
3. Put in numbers. Δ P = 2.15 × 10⁹ × 2 × 10⁻³ = 4.3 × 10⁶ N m⁻² = 43 × 10⁵ N m⁻².
4. So. Comparing with P × 10⁵ N m⁻² gives P = 43.

The common slip: 4300. Using 0.2 as the strain instead of 0.2/100 gives 4.3 × 10⁸ N m⁻², so P comes out as 4300, not 43.

The idea to keep. Every elastic modulus is stress divided by strain. For bulk modulus the stress is the extra pressure and the strain is Δ V/V. Turn a percentage into a fraction before you multiply.

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