A metallic bar of Young's modulus, <math> <mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></msup> N <msup><mrow>m</mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow> </math> and coefficient of linear thermal expansion <math> <mrow> <mn>1</mn> <msup> <mrow> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mo>∘</mo> </mrow> </msup> <msup> <mrow> <mi>C</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math> , length 1 m and area of cross-section <math> <mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup> <msup><mrow>m</mrow><mrow><mn>2</mn></mrow></msup></mrow> </math> is heated from <math> <mrow> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>?</mo> </mrow> </msup> <mi>C</mi> </mrow> </math> to <math> <mrow> <mn>1</mn> <mn>0</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>?</mo> </mrow> </msup> <mi>C</mi> </mrow> </math> 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, <math> <mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mn>1</mn></mrow></msup>&nbsp;N&nbsp;<msup><mrow>m</mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow> </math> and coefficient of linear thermal expansion <math> <mrow> <mn>1</mn> <msup> <mrow> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> <mrow> <mo>∘</mo> </mrow> </msup> <msup> <mrow> <mi>C</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math> , length 1 m and area of cross-section&nbsp; <math> <mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup>&nbsp;<msup><mrow>m</mrow><mrow><mn>2</mn></mrow></msup></mrow> </math> is heated from <math> <mrow> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>?</mo> </mrow> </msup> <mi>C</mi> </mrow> </math> to <math> <mrow> <mn>1</mn> <mn>0</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>?</mo> </mrow> </msup> <mi>C</mi> </mrow> </math> &nbsp;without expansion or bending. The compressive force developed in it is :

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Physics Class 11th Physics Mechanical Properties of Fluids

A metallic bar of Young's modulus, $0.5 \times 1 0^{11} N m^{- 2}$ 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 -

$5 * 1 0^{3} N$

Option 2 -

$50 * 1 0^{3} N$

Option 3 -

$100 * 1 0^{3} N$

Option 4 -

$2 * 1 0^{3} N$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

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

$\Rightarrow$ Longitudinal strain, $δ = 1 0^{- 5} \times 1 0^{2} = 1 0^{- 3}$

$\Rightarrow$ Compressive stress $= δ \times$ Young's Modulus

$= 1 0^{- 3} \times 0.5 \times 1 0^{11}$

$= 0.5 \times 1 0^{8}$

$\Rightarrow$ Compressive force $= 0.5 \times 1 0^{8} \times 1 0^{- 3} = 0.5 \times 1 0^{5}$

$= 5 \times 1 0^{4} \times \frac{10}{10}$

$= 50 \times 1 0^{3} N$

Thermal strain <math> <mrow> <mo>=</mo> </mrow> </math> Longitudinal strain <math> <mrow> <mo>=</mo> <mi>α</mi> <mi>Δ</mi> <mi>T</mi> </mrow> </math>  <math> <mrow> <mo>⇒</mo> </mrow> </math> Longitudinal strain, <math> <mrow> <mi>δ</mi> <mo>=</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>  <math> <mrow> <mo>⇒</mo> </mrow> </math> Compressive stress <math> <mrow> <mo>=</mo> <mi>δ</mi> <mo>×</mo> </mrow> </math>  Young's Modulus <math> <mrow> <mo>=</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mo>×</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </msup> </mrow> </math>  <math> <mrow> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> </mrow> </math>  <math> <mrow> <mo>⇒</mo> </mrow> </math> Compressive force <math> <mrow> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>5</mn> </mrow> </msup> </mrow> </math>  <math> <mrow> <mo>=</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> <mo>×</mo> <mfrac> <mrow> <mn>1</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </mfrac> </mrow> </math>  <math> <mrow><mo>=</mo><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>

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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 :