Question

brass wire of length 1 metre and area of cross section 1 millimetre square is is stretched by applying force of 20 Newtons then the work done per unit volume is​

Answer 1

Given info : A brass wire of length 1 metre and area of cross section 1 millimetre square is is stretched by applying force of 20 Newtons.

To find : the workdone per unit volume.

Solution : experimentally, Young's modulus of brass = 10¹¹ N/m²

now, we know, Young's modulus = stress/strain

so, Y = stress/strain

⇒strain = stress/Y ......(1)

Work done per unit volume of stretching wire is given by, U = 1/2 × stress × strain

from equation (1) we get,

U = 1/2 × stress²/Y

Stress = force applied /area

= 20N/(1mm²) = 20 × 10⁶ N/m²

So, U = 1/2 × 400 × 10¹²/10¹¹ = 2000 J/m³

Therefore the workdone per unit volume is 2000 J/m³.