JEE PYQ: Properties Of Matter Question 16
Question 16 - 2019 (12 Apr 2019 Shift 2)
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:
(1) $9F/(\pi r^2 YT)$
(2) $6F/(\pi r^2 YT)$
(3) $3F/(\pi r^2 YT)$
(4) $F/(3\pi r^2 YT)$
Show Answer
Answer: (3)
Solution
$\Delta l_{\text{comp}} = \Delta l_{\text{thermal}}$: $\alpha = \frac{F}{\pi r^2 YT}$
Coefficient of volume expansion: $\gamma = 3\alpha = \frac{3F}{\pi r^2 YT}$
BETA
