JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Elasticity & SHM

When a rubber ball is taken to a depth of _____ m in deep sea, its volume decreases by

0.5%

.
(The bulk modulus of rubber

= 9.8 \times 1 0^{8} Nm^{- 2}

Density of sea water

= 1 0^{3} kgm^{- 3}

g = 9.8 m/s^{2}

)

Answer: 500

Solution

The bulk modulus relates the pressure increase to the fractional volume change:

B = \frac{Δ P}{∣Δ V / V ∣}

. At depth

h

the excess pressure is

Δ P = ρ g h

, so

ρ g h = B ∣Δ V / V ∣

. Solving for the depth,

h = \frac{B ∣Δ V / V ∣}{ρ g} = \frac{9.8 \times 1 0 ^{8} \times 0.005}{1 0 ^{3} \times 9.8} .

This gives

h = 500

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Integer answer