The fractional compression ( (Δ V)/V ) of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = 2 × 10⁹ N m⁻², density of water = 10³ kg m⁻³, acceleration due to gravity g = 10 m s⁻².

Solution

Physics sir · 3 steps

Find the extra pressure at that depth, then divide it by the bulk modulus.

1. Extra pressure. The water at the surface already sits at atmospheric pressure. What squeezes it more at depth is the extra pressure from the water column above, Δ P = ρ g h.
2. Put in numbers. Δ P = 10³ × 10 × 2500 = 2.5 × 10⁷ N m⁻², taking h = 2.5 km = 2500 m.

   (Δ V)/V = (Δ P)/B = (2.5 × 10⁷)/(2 × 10⁹) = 1.25 × 10⁻²

3. So. The fractional compression is 1.25 × 10⁻². Multiplied by 100, that is 1.25%, option (b).

The idea to keep. Bulk modulus links the pressure change to the volume change: Δ V/V = Δ P/B. Under water, Δ P = ρ g h. Convert km to m first, and multiply by 100 at the end for a percentage.

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