A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01 % whereas the liquid gets compressed to 0.03 %. The ratio of Bulk modulus of water to that of the liquid is 3/x. The value of x is ____________.

Solution

Physics sir · 4 steps

Same pressure on both, so bulk modulus goes inversely with the fractional squeeze. The volumes do not matter.

1. Bulk modulus. Bulk modulus compares the pressure applied with the fractional change in volume it causes. A stiffer liquid squeezes by a smaller fraction.

   B = P/(Δ V / V)

2. Read the strains. The percentages already are Δ V/V. Water gives Δ V/V = 0.01% = 1 × 10⁻⁴ and the liquid gives 0.03% = 3 × 10⁻⁴. The 1 litre and 2 litre values are not needed.
3. Take the ratio. P is the same for both, so it cancels: B_w/Bₗ = (3 × 10⁻⁴)/(1 × 10⁻⁴) = 3.
4. So. 3/x = 3, which gives x = 1.

The common slip: 0.5. Using the absolute volume changes (10⁻⁴ L for water, 6 × 10⁻⁴ L for the liquid) instead of the fractional ones makes the ratio 6 and gives x = 0.5.

The idea to keep. Elastic moduli always use strain, the fractional change, never the raw change. With the same stress, the modulus is inversely proportional to the strain.

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