Question

A wire has a young’s modulus of 10^5N/m^2, length 1m & radius 3mm. Assuming a uniform cross sectional area, find the radius of wire after it is under a force of 1N from both ends.

(a) 2.58m

(b) 2.30m

(c) 3.54m

(d) 2.24m

I had been asked this question by my school principal while I was bunking the class.

The question is from Solids Mechanical Properties topic in chapter Mechanical Properties of Solids of Physics – Class 11

Answer 1

Correct choice is (a) 2.58m

Easiest explanation: Force = 1N. Initial area = πr^2 = 2.82*10^-5m^2.

Stress = Y*Strain

Δl = F/A * l/Y = (1/2.82*10^-5)*(1/10^5) = 0.35m

As volume will remain same (we can also say that product of l & r^2 will be constant as other terms in expression of volume are constants).

 1*3^2 = 1.35*R^2

 ⇒R = 2.58m.