A copper wire of 25cm length is fixed by means of supports at it's ends. Supports can yield by 0.01 cm, if the temperature of the bar is raised by 100°C, then the strain induced in bar for alpha=20×10^-6/°C and E=1×10^6Kg/cm^2,will be

Solution(By Examveda Team)

Correct Answer:
To find the strain induced in the copper wire, we'll use the formula for linear expansion:
ΔL = α * L * ΔT
Where:
ΔL = Change in length
α = Coefficient of linear expansion (given as 20×10^-6/°C)
L = Original length of the wire (25 cm)
ΔT = Change in temperature (given as 100°C)
Given that the supports can yield by 0.01 cm, we need to consider this while calculating the strain. The total change in length should be less than 0.01 cm.
So, rearranging the formula:
ΔL = α * L * ΔT
ΔL = (20×10^-6/°C) * (25 cm) * (100°C)
ΔL = 0.05 cm
However, since the supports can only yield by 0.01 cm, the actual change in length will be limited to 0.01 cm. Hence, the strain induced is:
Strain = (Change in length) / (Original length)
Strain = (0.01 cm) / (25 cm)
Strain = 0.0004