A wire of length L and radius a rigidlyl fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is L, if another wire of same material but of length 2 L and radius 2 a is stretched with a force 2 F, the increase in its length will be

Options

A. L/4
B. L
C. L/2
D. 2L

Answer

b

Explanation

Young's modulus `Y = (FL)/(AI) = (FL)/(pi a^(2) I)`
since for same material Young's modulus is same, ie.,
`Y_(1) = Y_(2)` or `(FL)/(pi a^(2) I) = ((2F)(2L))/(pi (2a)^(2) r) implies r = 1`