A wire is replaced by another wire of same length and material but of twice diameter.
(i) What will be the effect on the increases in its length under a given load?
(ii) What will be the effect on the maximum load which it can bear?

Explanation

Young's modulus,
`Y=(Mgl)/(pir^(2).Deltal)=(Mgl)/(pi((D)/(2))^(2)Deltal)=(4Mgl)/(piD^(2).Deltal)`
where, D is the diameter of the wire.
`therefore` Elongation, `Deltal=(4Mgl)/(piD^(2).Y)` i.e. `Deltal prop (1)/(D^(2))`
Clearly ,if the diameter is doubled, the elongation will become one-fourth.
Also, maximum stress, `sigma_(m)=(M_(m)g)/((piD^(2)//4))` or `M_(m) prop D^(2)`
Clearly, if the diameter is doubled , the wire can support four times the original load.