Question

A copper rod length l and radius r us suspended from the ceiling

Answer 1

Answer:

your question is incomplete without much information

Answer 2

Your complete question is -

A copper rod of length  L  and radius  r  is suspended from the ceiling by one of its ends. What will be elongation of the rod due to its own weight when   ρ  and  Y  are the density and Young's modulus of the copper respectively?

ρgL²/2Y is the elongation of the rod due to its own weight.

Given-

• Length of the copper rod = L
• Radius of the copper rod = r
• Density of the copper = ρ
• Young's modulus of the copper = Y

We know that weight of the rod can be given by -

W = V × ρ × g where V = A × L so,

W = A × L × ρ × g

The average value of force when weight increases linearly will be-

F av = W/2

F av = A × L × ρ × g /2

We know that stress is the ratio of force per unit area and Strain is δL/L

Young's modulus is the ratio of stress upon strain. Therefore elongation is

δL = F × L/ A × Y

By substituting the value we get

δL = A × L × ρ × g × L / 2 A Y

δL = ρgL²/2Y