A metallic bar of Young's modulus, and coefficient of linear thermal expansion , length 1 m and area of cross-section is heated from to without expansion or bending. The compressive force developed in it is: [2024]

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Solution

Q.
A metallic bar of Young's modulus, $0.5 \times 10^{11}$ $N$ $m^{- 2}$ and coefficient of linear thermal expansion $10^{- 5} ° C^{- 1}$ , length 1 m and area of cross-section $10^{- 3}$ $m^{2}$ is heated from $0 ° C$ to $100 ° C$ without expansion or bending. The compressive force developed in it is: [2024]

1 $5 \times 10^{3}$ N

2 $50 \times 10^{3}$ N

3 $100 \times 10^{3}$ N

4 $2 \times 10^{3}$ N

Ans.
(2)

$Y = 0.5 \times 10^{11} {N/m}^{2}, α = 10^{- 5} / ° C$

$l = 1 m, A = 10^{- 3} m^{2}, Δ T = 100 ° C$

$F = Y A α Δ T$

$F = 0.5 \times 10^{11} \times 10^{- 3} \times 10^{- 5} \times 100$

$F = 50 \times 10^{3} N$

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