Question

A steel wire is stretched by a certain amount under a load. if the load and the radius both are increasing to 4 times find the stretch cause in wire

Answer 1

Young's Modulus = γ = W/A × L/l
W:load
A:Area of cross section
L:original length
l:elongation

⇒ Elongation = l = WL/Aγ
⇒Elongation = l = WL/πr²γ (∵A = πr²) .......... (1)
When both load and radius are increased to four times, the elongation becomes,
l' = 4WL / (4r)²πγ
l' = WL / 4πr²γ
l' = l / 4 (using equation (1) )
Which is the required answer