A wire stretches by a certain amount under a load. If the load and radius are increased to four times, find the stretch caused in the wire.

Options

A. l
B. `(l)/(2)`
C. `(l)/(3)`
D. `(l)/(4)`

Answer

D

Explanation

Young's modulus, `Y = (W)/(A) xx (L)/(l)`
`therefore` Elongation , `l = (WL)/(AY) = (WL)/(pir^(2)Y)=(l)/(4)`
When both load and radius are increased to four times, the elongaation becomes
` l' = (4W xx L)/(pi(4r)^(2) xxY) = (WL)/(4pir^(2)Y) = (l)/(4)`