A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

 

  • Option 1)

    9F/(\pi r^{2}YT)

     

  • Option 2)

    6F/(\pi r^{2}YT)

  • Option 3)

    3F/(\pi r^{2}YT)

  • Option 4)

    F/(3\pi r^{2}YT)

 

Answers (1)

 

Coefficient of Linear Expansion -

\alpha=\frac{\Delta L}{L_{0}\Delta T}

- wherein

Unit of \alpha is C-1 or  K-1

 

 

Y\alpha T=\frac{F}{\pi r^{2}}

\alpha =\frac{F}{\pi r^{2}YT}

\wp =3\alpha

\wp =\frac{3F}{\pi r^{2}YT}


Option 1)

9F/(\pi r^{2}YT)

 

Option 2)

6F/(\pi r^{2}YT)

Option 3)

3F/(\pi r^{2}YT)

Option 4)

F/(3\pi r^{2}YT)

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