JEE Main 2022 · 24 June · morning · Single correct · +4 / −1
The bulk modulus of a liquid is 3 × 10¹⁰ Nm⁻². The pressure required to reduce the volume of liquid by 2% is :
- (a) 3 × 10⁸ Nm⁻²
- (b) 9 × 10⁸ Nm⁻²
- (c) 6 × 10⁸ Nm⁻²
- (d) 12 × 10⁸ Nm⁻²
Answer and solution
Answer (c) 6 × 10⁸ Nm⁻²
Solution
Physics sir · 4 steps
Bulk modulus is pressure per unit fractional volume change, so pressure is just B times 0.02.
- Definition. Bulk modulus compares the extra pressure on a body with the fractional change in its volume that this pressure causes. The minus sign only says that volume goes down when pressure goes up.
B = (Δ P)/(-Δ V / V) ⇒ Δ P = B × (|Δ V|)/V
- Strain as a number. A 2% decrease in volume means (|Δ V|)/V = 2/100 = 0.02. Strain has no unit, so use this decimal, not the 2.
- Put in numbers. Δ P = 3 × 10¹⁰ × 0.02 = 6 × 10⁸ N m⁻².
- So. The pressure needed is 6 × 10⁸ N m⁻², which is option (c).
The idea to keep. Every elastic modulus is stress divided by strain. Turn a percentage strain into a decimal first, then stress is just modulus times strain.
Answer from the NTA final answer key. Solution by PrepWiser.