Ncert Exercises & Solutions

Q.20 A steel rod $(Y = 2.0 \times 10^{11} N / m^{2} and α = 10^{- 50} ° C^{- 1})$ of length 1 m and area of cross-section $1 {cm}^{2}$ is heated from $0 ° C to 200 ° C$ without being allowed to extend to bend. What is the tension produced in the rod?

Hint: The tension produced in the rod can be calculated by the stress developed in the wire.

Step 1: Find the tension produced in the wire.

Given, Young's modulus of steel, Y

= 2.0 \times 10^{11} N / m^{2}

Coefficient of thermal expansion,

α = 10^{- 5} ° C^{- 1}

Length, l=1m

Area of cross-section, A

= 1 {Cm}^{2} = 1 \times 10^{- 4} m^{2}

Increases in temperature,

∆ T = 200 ° C - 0^{°} C = 200 ° C

The tension produced in steel rod(F) =

YAα ∆ T

= 2.0 \times 10^{11} \times 1 \times 10^{- 4} \times 10^{- 5} \times 200

= 4 \times 10^{4} N

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