Q 11-10-015NEETJEE MainEAMCET 2013 (Medical)Medium
A long cylindrical metal vessel, of coefficient of linear expansion $\alpha$, is filled with a liquid up to a certain height. On heating, the level of the liquid in the cylinder remains the same. The volume coefficient of expansion of the liquid is
Answer: (A) $2\alpha$
Concept. Liquid volume $=$ base area $\times$ height. If the height stays fixed, the liquid's volume grows only as fast as the vessel's area, whose coefficient is $2\alpha$.
Step 1. Equate. $\gamma_{\text{liquid}}V\Delta T = 2\alpha V\Delta T$, so $\gamma_{\text{liquid}} = 2\alpha$.
Answer. $2\alpha$ (Option A).
Solution by Sreeraj P, M.Sc Physics