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  • Help me solve this - A rod, of length L at room temperature and uniform area of cross section A, is made of a metal havin - Properties of Solids and Liquids - JEE Main

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion \alpha /^{o}C. It is observed that an external copressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by \Delta TK. Young's modulus, Y , for this metal is:

 

  • Option 1)

    \frac{F}{A\alpha \Delta T}

  • Option 2)

  • Option 3)

    \frac{F}{2A\alpha \Delta T}

  • Option 4)

    \frac{2F}{A\alpha \Delta T}

Answers (2)

best_answer

 

Elongation -

\Delta l= \frac{FL}{AY}

 

- wherein

\Delta l= Elongation

y = \frac{\frac{F}{A}}{\frac{\Delta L}{L}}

Coefficient of linear expansion

d = {\frac{\Delta L}{L \Delta T}}

y =\frac{F}{Ad \Delta T}

 

 


Option 1)

\frac{F}{A\alpha \Delta T}

Option 2)

Option 3)

\frac{F}{2A\alpha \Delta T}

Option 4)

\frac{2F}{A\alpha \Delta T}

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