For a wire of length L, maximum change in length under stress condition is 2 mm. What is the change in length under same conditions when length of wire is halved?

Options

A. 1 mm
B. 2 mm
C. 4 mm
D. 8 mm

Answer

a

Explanation

Young's modulus, `Y = ("Longitudinal stress")/("Longitudinal strain") = (F//A)/(I//L)`
Where, F is force, A is area, I is change in length and L is original length.
Case I `Y = (F//A)/(2//L)`
Case II `Y = (F//A)/(I//L//2)`
Equating Eqs. (i) and (ii) we get
`(L)/(2) = (L//2)/(I) implies I = 1 mm`