Properties Of Solids And Liquids Question 543
Question: The volume of a metal ball increases by 0.18% when its temperature is increased by $ 30^{o}C $ What is the coefficient of linear expansion of metal?
Options:
A) $ 2\times {{10}^{-5}}l^{0}C $
B) $ 3\times {{10}^{-5}}l^{0}C $
C) $ 6\times {{10}^{-5}}l^{0}C $
D) $ 1.8\times {{10}^{-4}}l^{0}C $
Show Answer
Answer:
Correct Answer: A
Solution:
Increase in volume of ball $ \Delta V=V\gamma \Delta T $
$ \frac{\Delta V}{V}=\gamma \Delta T $
$ \frac{\Delta V}{V}=\frac{0.18}{100} $ and $ \Delta T=30{{}^{0}}C $
$ \therefore $ $ \gamma =\frac{\Delta V}{V\Delta t}=\frac{0.18}{100\times 30}=6\times {{10}^{-5}} $ per $ ^{0}C $
$ \alpha =\frac{\gamma }{3}=\frac{6\times {{10}^{-5}}}{3}=2\times {{10}^{-5}} $ per $ {{}^{0}}C $
