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

Answer

B

Explanation

We know `Y=(stress)/(strai n)=((F)/(A))/((trianglel)/(l))`
`impliesY=(Ftrianglel)/(Al)=(Fl)/(Atrianglel)`
For `1^(st)` wire: `Y=(F_1l_1)/(Atrianglel)` .(i)
For `ii^(nd)` wire: `Y=(F_2l_2)/(3Atrianglel)` ..(ii)
As volume of the wires is same
Hence, `Al_1=3Al_2`
or `(l_1)/(l_2)=3` .(iii)
From (i) and (ii), `(F_1)/(F_2)=(l_2)/(3l_1)` .(iv)
From (iii) and (iv), `(F_1)/(F_2)=(1)/(9)` or `F_2=9F_2`