Q. 29

A steel rod is rigidly clamped at its two ends. The rod is under zero tension at 20°C. If the temperature rises to 100°C, what force will be rod exert on one of the clamp? Area of cross section of the rad = 2.00 mm2. Coefficient of linear expansion of steel = 12.0 × 10–6 °C–1 and Young’s modulus of steel = 2.00 × 1011 N m–1.

Answer :


Given:

Temperature at which rod is under zero tension : T1 = 20 ° C.

Increased Temperature : T2 = 100 ° C.
Change in temperature : Δ T= T2 – T1 = 100-20 = 80 ° C.
Area of cross section of the rod : A = 2.00 mm2 = 2.00 × 10-6 m2.


Coefficient of linear expansion of steel : α = 12.0 × 10–6 °C–1


Young’s modulus of steel: Y = 2.00 × 1011 N m–1.
Formula used:


We need to find the force on the clamps by the rod when the rod undergoes thermal expansion due to increase in temperature.


Formula for Linear Expansion:


Here, L’ is the changed length at T2 and L is the original length of the rod at T1.


Thus, Change in length is


We get:



Formula for Young’s Modulus is:



Substituting Δ L:



Hence when the temperature is increased to 100° C , the rod will exert a force of 384N on one of the champ.


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