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The bulk modulus of a liquid is 3×10¹⁰ N m⁻². The pressure required to reduce the volume of the liquid by 2% is

Asked in JEE Main 24th June 1st Shift 2022 · Bulk modulus and compressibility

(1) 3×10⁸ N m⁻²
(2) 9×10⁸ N m⁻²
(3) 6×10⁸ N m⁻²
(4) 12×10⁸ N m⁻²

Answer: (3) 6×10⁸ N m⁻²

Step-by-step solution

Given: B=3×10¹⁰ N m⁻² and (Δ V)/V=2%=2×10⁻².

B=(Δ P)/(|(Δ V)/V|), so Δ P=B|(Δ V)/V|.

Δ P=3×10¹⁰×2×10⁻².

Δ P=6×10⁸ N m⁻².

Why the other options are wrong

(1) comes from reading 2% as 1%, that is, using (Δ V)/V=10⁻²; it is half of the correct value.
(2) comes from treating the 2% as a linear strain and cubing the length change, so the volume strain is taken as 3×10⁻² instead of 2×10⁻².
(4) comes from doubling twice, once for the 2% and once more as if the volume strain were 4×10⁻²; the percentage needs to be divided by 100 only once.

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