Question

Two wires of the same material and same length but diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio

Answer 1

it is based on mechanical properties of matters.
we know, potential energy per unit volume = 1/2 × stress × strain.

it is given that, both wires are made by same material, length of wires are same and also same force applied to the end of wire . hence, strain of both wires will be same.

we know as well,
strain = stress/Y
where Y is Young's modulus.

so, potential energy per unit volume = 1/2 × (stress)²/Y

but we know, stress is inversely proportional to square of diameter of wire.

so, potential energy per unit volume is inversely proportional to (diameter)⁴.

so, ratio of potential energy per unit volume = $\left(\frac{d_2}{d_1}\right)^4$

given, $d_1:d_2=1:2$

so, ratio of potential energy per unit volume = 2⁴/1⁴ = 16/1

Answer 2

Answer:

Hope it will help you buddy .....

I think u can mote easily understand by 2nd pic