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

Answer

A

Explanation

Young.s modulus, `Y = (Fl)/(A Delta l)`
Since initial volume of wire are same
`:.` Their areas of cross sections are A and 3A and length are 3l and l respectively. For wire 1.
`Delta l= ((F)/(AY)) 3l` …(i)

For wire2, let F. force is applied
`(F.)/(3A) = Y (Delta l)/(l) rArr Delta l= ((F.)/(3AY))l` ..(ii)

From equation (i) and (ii), `((F)/(AY)) 3l= ((F.)/(3AY))l rArr F. = 9F`