Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by `Deltax` on applying force F, how much force is needed to stretch wire 2 by the same amount?

Options

A. 4F
B. 6F
C. 9F
D. F

Answer

C

Explanation

From Hooke's laws
`F= (YA Delta l)/(l)`
or `F= (YA'Delta l)/((Al))= (YA^(2) Delta l)/(V)`
`F prop A^(2) rArr F prop (3A)^(2)`
`(F^(1))/(F) = 9 rArr F'= 9F`