Question

A wire is stretched by a certain amount under a load. if the load and the radius both are increased to four times find the strech caused in the wire

Answer 1

Young's Modulus = γ = W/A x L/l
⇒ 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.

Answer 2

Answer:

The answer is Δl/4

Step-by-step explanation:

Young's modulus ,

Y= F / πr² × l / Δl or Δl = Fl / πr²Y

When F'=4F and r'=4r , then

Δl' = (4F)l / π(4r)²×Y

∴ Δl' / l = l / 4  

or

 → Δl'= Δl/4 .

Hope it helps you.....