A solid sphere having a bulk modulus of 2.0 10^9 N m ⁻² is lowered to the bottom of a lake. If its volume decreases by 0.05 % , the depth of the lake is : (Given: density of lake water = 1000 kg m ⁻³ , g = 10 m s ⁻² )

Step-by-step solution

The fractional change in volume (volumetric strain) is: V V = 0.05 100 = 5 10⁻⁴ The hydrostatic pressure applied on the sphere is given by the bulk modulus formula: P = B V V P = (2.0 10^9) (5 10⁻⁴) = 10^6 N m ⁻² The pressure at a depth h in the lake is given by P = g h . Equating the two expressions for pressure: 10^6 = 1000 10 h h = 100 m Answer: 100 m