A solid block of initial volume 6 10⁻³ m ^3 is taken to a depth of 2000 m in a lake. The bulk modulus of the material of the block is 4 10¹⁰ N m ⁻² . The elastic potential energy stored in the block due to the increased pressure is _____ J. (Take the density of water as 10^3 kg m ⁻³ and g = 10 m s ⁻² )

Step-by-step solution

The hydrostatic pressure exerted on the block at depth h is: P = _w g h P = 10^3 10 2000 = 2 10^7 N m ⁻² The elastic potential energy U stored in a compressed volume is given by: U = 1 2 stress strain V Since strain = P B and stress = P , we can write: U = ( P)^2 V 2B Substituting the given values: U = (2 10^7)^2 6 10⁻³ 2 4 10¹⁰ U = 4 10¹⁴ 6 10⁻³ 8 10¹⁰ U = 24 10¹¹ 8 10¹⁰ = 30 J Answer: 30