Ncert Exercises & Solutions

Q.20 A steel rod $(Y = 2.0 \times 10^{11} N / m^{2} and α = 10^{- 50} ° C^{- 1})$ $(Y = 2.0 \times 10^{11} N / m^{2} and α = 10^{- 50} ° C^{- 1})$ of length 1 m and area of cross-section $1 {cm}^{2}$ $1 {cm}^{2}$ is heated from $0 ° C to 200 ° C$ $0 ° C to 200 ° C$ 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}

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

Coefficient of thermal expansion,

α = 10^{- 5} ° C^{- 1}

$α = 10^{- 5} ° C^{- 1}$

Length, l=1m

Area of cross-section, A

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

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

Increases in temperature,

Δ T = 200 ° C - 0^{\circ} C = 200 ° C

$∆ T = 200 ° C - 0^{°} C = 200 ° C$

The tension produced in steel rod(F) =

YAα Δ T

$YAα ∆ T$

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

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

= 4 \times 10^{4} N

$= 4 \times 10^{4} N$

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