A uniform cylindrical rod of length L and radius r , is made from a material whose Young's modul

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10-1.Thermometry, Thermal Expansion and Calorimetry

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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) equals to

A

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

B

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

C

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

D

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

(JEE MAIN-2019)

Solution

Lenght of cylinder remains unchanged

So ${\left( {\frac{F}{A}} \right)_{compressive}} = {\left( {\frac{F}{A}} \right)_{Themal}}$

$\frac{F}{{\pi {r^2}}} = Y\alpha T\,\,\,\,\,\,\left( {\alpha \,is\,liner\,coefficient\,of\,\exp ansion} \right)$

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

$\therefore \,The\,coefficient\,of\,volume\,expansion\,\gamma = 3\alpha $

$\therefore \gamma =3 \frac{F}{{YT\pi {r^2}}}$

Standard 11

Physics

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