Two metal wires P and Q of same length and material are stretched by same load. Yheir masses are in the ratio `m_(1):m_(2)`. The ratio of elongation of wire P to that of Q is

Options

A. `m_(1)^(2):m_(2)^(2)`
B. `m_(2)^(2):m_(1)^(2)`
C. `m_(2):m_(1)`
D. `m_(1):m_(2)`

Answer

C

Explanation

We know that, Young's modulus `(Y)=(Fl)/(ADeltal)rArrDelta=(Fl)/(AY)`
where, A=area of cross-section of wire
`Deltal`=change in the length of the wire,
l=length of the wire
and F= applied force.
According to the question, F, l and Y are same for both wires, i.e.
`Deltalprop(1)/(A)` . . . .(i)
But `m=rhoV`
where, `rho`=density, V = volume.
`m=rhoAl" "[becauseV=Al]`
`mpropA` . . .(ii)
From Eqs. (i) and (ii), we get
`(Deltal_(1))/(Deltal_(2))=(A_(2))/(A_(1))=(m_(2))/(m_(1))`