Question

The area of cross-section of a metal-rod is 1 cm. It
is clamped tightly at its two ends at 0°C. The rod is
heated to 100°C. Calculate the tension produced
at its two ends. Coefficient of linear expansion of
metal is 1.2 x 10-5 °c) and Young's modulus is
2.0 x 1011 Nm-2
Ans. 2.4 x 104 N.​

Answer 1

Explanation:

Let be increase in the length of the rod due to increase in temperature of the rod. Then

where, is the coefficient of the linear expansion, is the rise in temperature and L is the length of the rod.

Let the compressive tension of the rod be T and A becross-section area. Then

(Using (i))

Here,