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 `/_\x` on applying force 1 newton, 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

`V = A_(1)L_(1) = A_(2)L_(2) :. (L_(2))/(L_(1)) = (A_(1))/(A_(2)) = (1)/(3)`
`Y = (F_(1)L_(1))/(A_(1)Delta x) = (F_(2) L_(2))/(A_(2) Delta x)`
`:. F_(2) L_(2) A_(1) = F_(1) L_(1)A_(2)`
`:. F_(2) = ((L_(1) A_(2))/(L_(2)A_(1)))F_(1) = ((3)/(1)) xx ((3)/(1))F_(1) :. F_(2) = 9 F`