Question

the work done per unit volume to stretch the length of area of cross section 2mm^2 by 2% will be (Y=8*10^10N/m^2

Answer 1

The total work done in stretching a material per unit volume by 2% length will be 16 MJ/m³

Explanation :

Given,

young's modulus, Y = 8 x 10¹⁰ N/m²

percentage change in length, ΔL/L = 2% = 2/100

we know that the total work done in stretching a material is given by,

U = 1/2 x Y x (ΔL/L)² x V

hence work done per unit volume

= U/V

= 1/2 x Y x (ΔL/L)²

= 1/2 x 8 x 10¹⁰ x (2/100)²

= 16 x 10⁶ joules/m³

= 16 MJ/m³

Hence the total work done in stretching a material per unit volume by 2% length will be 16 MJ/m³