Two wires are made of the same material and has 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 ax 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

Two wire will have some value of Young.s modulus Y Also as volume remains same, so wire of area of crosssection will have length r/3
For wire 1,
`Y=(Fl)/(ADeltaX)` ..(1)
For wire 2
`Y=(F_(l)xxl/3)/(3ADeltax)` …(2)
From 1 and 2
`(Fl)/(ADeltax)=(F^(l)l)/(9ADeltax)` `F_(1)=9F`
So Correct choice is (c).