Question

A certain wire stretches 1.3 cm when a force F of magnitude 1000 N is applied to it. The same force is applied to a second wire of the same material but with twice the diameter and twice the length. In cm, the second wire stretches:

Answer 1

Since the same wire is used in both cases, Young's modulus of the wire in both cases will be the same. The Young's modulus is given by,

where,

F is the force

A is the area cross section of the wire.()

l is the original length

Case 1

Case 2

Equate (1) and (2), Therefore

Given,

(Ans.)