JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry

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

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Correct Answer

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

Detailed explanation

Lenght of cylinder remains unchanged

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

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

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

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

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

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