Question

When a block of mass M is suspended by a long wire of lenght L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is:

Answer 1

elastic Potential energy per unit volume is given by, U = 1/2 × stress × strain

Let volume of wire is V , cross sectional area is A and length of wire is already given i.e., L

so, elastic potential energy = 1/2 × stress × strain × V

now, stress = force applied/area

= weight of body/A

= Mg/A

and strain = change in length/original Length

= l/L

so, elastic potential energy = 1/2 × Mg/A × l/L × AL

= 1/2 × Mg × l

= 1/2 Mgl

hence, elastic potential energy is 1/2Mgl