A rubber ball is taken to a depth h in a lake, which causes its volume to decrease by 0.1 % . The bulk modulus of rubber is 2 10^9 N m ⁻² . If the density of lake water is 1000 kg m ⁻³ and acceleration due to gravity is 10 m s ⁻² , the value of h (in meters) is

Step-by-step solution

The fractional decrease in the volume of the rubber ball is: V V = 0.1 100 = 10⁻³ The increase in pressure P required to cause this volume change is related to the bulk modulus B by: P = B ( V V ) Substituting the given values: P = 2 10^9 10⁻³ = 2 10^6 N m ⁻² This pressure increase is provided by the hydrostatic pressure of the water at depth h : P = g h Equating the two expressions for P : 2 10^6 = 1000 10 h 2 10^6 = 10^4 h Solving for h : h = 2 10^6 10^4 = 200 m . Answer: 200