# NCERT Class 11 Physics Solutions: Chapter 11 – Thermal Properties of Matter-Part 4

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**Question 11.9:**

A brass wire long at is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of , what is the tension developed in the wire, if its diameter is Co-efficient of linear expansion of brass Young’s modulus of brass

**Answer:**

Initial temperature,

Length of the brass wire at

Final temperature,

Diameter of the wire,

Tension developed in the wire

Coefficient of linear expansion of brass,

Young’s modulus of brass,

Young’s modulus is given by the relation:

Tension developed in the wire

Area of cross>section of the wire.

Change in the length, given by the relation:

Equating equations we get:

(The negative sign indicates that the tension is directed inward.)

Hence, the tension developed in the wire is

**Question 11.10:**

A brass rod of length and diameter is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at , if the original lengths are at ? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass

**Answer:**

Initial temperature,

Final temperature,

Change in temperature,

Length of the brass rod at

Diameter of the brass rod at

Length of the steel rod at

Diameter of the steel rod at

Coefficient of linear expansion of brass,

Coefficient of linear expansion of steel,

For the expansion in the brass rod, we have:

For the expansion in the steel rod, we have:

Total change in the lengths of brass and steel,

Total change in the length of the combined rod

Since the rod expands freely from both ends, no thermal stress is developed at the junction.