A cable is replaced by another cable of the same length and material but of duouble the diameter.
(i) Under a given load which cable wil show greater extension?
(ii) How many times the second cable can support the maxium load without exceeding the elastic limit?

Explanation

(i) Young's modulus, `Y=(Mg)/((pi D^(2)//4)) xx l/(Deltal)`
or `Deltal = (4Mgl)/(pi D^(2)Y), i.e., Deltal prop (1)/(D^2)`
`:. (Deltal_2)/(Deltal_1) = (D_(1)^(2))/(d_(2)^(2)) = (d^2)/((2D_(1))^(2)) = 1/4 lt 1 or Deltal_(2) lt Deltal_(1)`
Thus elongation of first cable is greater than the second cable.
(ii) Maximum load a cable can support is
`W=(Deltal pi D^(2)Y)/(4l), i.e., W prop D^(2)`
`(W_2)/(W_1) = ((2D)^(2))/(D^2) = 4 or W_(2)= 4 W_(1)`.
There fore, the second cable wire all support 4 times the load supported by first cable wire.