Question

If a wire is stretched such that its radius is reduced to 1/n of it's original value, then its new resistance will increase to n^4 times; similarly resistance will decrease to n^4 times if radius is increased to n times by contraction.prove the above question please

Answer 1

sorry, but I think you got something wrong, it should be n^2, not n^4
This is due to the law relating resistance with relative resistance. Which is:

$R= \rho \frac{L}{A}$

where,
$\rho = relative resistance$
L=length of the wire, A= area of the cross section of the wire

if you reduce the wire's radius by 1/n, then according to the formula
$A= \pi r^2$
Area reduces by (1/n)^2, so resistance increases by n^2