Question

A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire be a constant force F is proportional to.......... 

(A) (1 / L²) 

(B) (1/L) 

(C) L² 

(D) L

Answer 1

Correct option: (C) L²

Explanation: 

Y = {(F/A) / (ℓ/L)} = (FL / Aℓ)

given : extension ℓ = x

ℓ = (FL / AY)  i.e. x = (FL / AY) = [{FL²} / {(AL)Y}]    .......(1)

as volume = V = Area × length

 i.e. V = AL

hence from (1) , x = (FL² / VY)

F is given to be constant, Y is constant. if volume is fixed then x ∝ L²