A ball falling in a lake of depth 200m shows a decrease of $0.1\%$ in its volume at the bottom.  What is the bulk modulus

Given Data:

• Depth of the lake (h) = 200 m
• Fractional decrease in volume (ΔV / V) = 0.1% = 0.001
• Density of water (ρ) = 1000 kg/m³
• Acceleration due to gravity (g) = 9.8 m/s²

The pressure at the bottom of the lake due to the water column is given by: 

ΔP = ρ · g · h

Substituting the values: 

ΔP = 1000 · 9.8 · 200 

ΔP = 1,960,000 Pa = 1.96 × 10⁶ Pa

Rearranging the formula for bulk modulus: 

B = -(ΔP) / (ΔV / V)

Substituting the values: 

B = -(1.96 × 10⁶) / (-0.001) 

B = 1.96 × 10⁶ × 100 

B = 1.96 × 10⁸ Pa

Final Answer:

The bulk modulus of the material of the ball is: 1.96 × 10⁸ Pa