Question

The young's modulus of a wire of length (L) and radius (r ) is Y. If the length is reduced to L/2 and radius r/2 , then its young's modulus will be

Answer 1

Young's modulus of wire is Y

•Young's modulus of a wire of length (L) and radius (r ) is Y

•Now , length is reduced to L/2 and radius r/2

L' = L/2 & R = r/2

• Also,

Stress = Y strain

F/A = (Y∆L)/L

F/πr² = (Y∆L)/L

Y = F.L/πr².∆L

• But , Young's modulus of wire depends upon material not on the physical dimensions & external conditions .

• This means, Length of wire has no effect on Young's modulus . so, change in length of wire doesn't affect the young's modulus of wire.

• After Changing length & radius the young's modulus of wire remains same i.e. Y

Answer 2

Answer: Y

Explanation: Young's modulus is a property of material and doesn't effected with change in length and diameter