A metallic bar of Young's modulus, 0.5*1011 N m−2 and coefficient of linear thermal expansion 1 0 − 5 ∘ C − 1 , length 1 m and area of cross-section 10−3 m2 is heated from 0 ? C to 1 0 0 ? C without expansion or bending. The compressive force developed in it is :

Thermal strain = Longitudinal strain = α Δ T ⇒ Longitudinal strain, δ = 1 0 − 5 * 1 0 2 = 1 0 − 3 ⇒ Compressive stress = δ * Young's Modulus = 1 0 − 3 * 0 . 5 * 1 0 1 1 = 0 . 5 * 1 0 8 ⇒ Compressive force = 0 . 5 * 1 0 8 * 1 0 − 3 = 0 . 5 * 1 0 5 = 5 * 1 0 4 * 1 0 1 0 =50*103 N

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

Option 1 - <math> <mrow><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup> N</mrow> </math>

Option 2 - <math> <mrow><mn>5</mn><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup> N</mrow> </math>

Option 3 - <math> <mrow><mn>1</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup> N</mrow> </math>

Option 4 - <math> <mrow><mn>2</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup> N</mrow> </math>

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 2

Detailed Solution:

Thermal strain $=$ Longitudinal strain $= α Δ T$