Answer
(a) $0.31cm$
(b) increase
Work Step by Step
(a) We can find the required diameter as follows:
$D=\sqrt{(\frac{4F}{\pi Y})}(\frac{L}{\Delta L})$
We plug in the known values to obtain:
$D=\sqrt{\frac{4(360N)(4.7m)}{\pi(20\times 10^{10}N/m^2)(0.0011m)}}$
$D=312.92\times 10^{-5}m$
$D=312.92\times 10^{-3}cm=0.31cm$
(b) We know that the cross sectional area of wire and its elongation are inversely proportional, hence the diameter should be increased.
