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. 4F
C. 6F
D. 9F

Answer

D

Explanation

Since, `Y= (F//A)/((Delta l)/(l)) = (Fl)/(A Delta l)`
`rArr Delta l= (Fl)/(AY) = (F(Al))/(A^(2)Y)`
`rArr Delta l= (FV)/(A^(2) Y)` [Volume (V) = Al]
`rArr F= (A^(2) Y Delta l)/(V)` [as `F prop A^(2)`]
`(F)/(F_(1))= ((A)^(2))/((3A)^(2))= (1)/(9) rArr F_(1)= 9F`