The resistance of a wire, of length 'l', is RΩ. The wire is stretched to double its length keeping the volume constant. The resistance of the wire will become?
4 R Ω
Here Volume = length×Area is constant. So if the wire is stretched to increase its length, its area will decrease proportionally i.e., if length is doubled then its area will be halved.
when length gets doubled l = 2l
area a = a/2
Therefore according to the formula, R=ρla
putting l = 2l and a = a/2, new resistance R' will be
R′=ρ2la/2
R′=ρl2×2a
R′=4(ρla)
R' = 4(R)
which will make the new resistance R' four times the initial value R.