Question

The volume of a metal sphere increases by $ \text{0}\text{.15 }\!\!%\!\!\text{ } $ when its temperature is raised by $ \text{24}{{\,}^{\text{o}}}\text{C}\text{.} $ The coefficient of linear expansion of metal is:

• A. $ 2.5\times {{10}^{-5}}/{{\,}^{o}}C $
• B. $ 2.0\times {{10}^{-5}}/{{\,}^{o}}C $
• C. $ 1.5\times {{10}^{-5}}/{{\,}^{o}}C\, $
• D. $ 1.2\times {{10}^{-5}}/{{\,}^{o}}C\, $

Answer 1

The Correct Option is B

Linear expansion coefficient $ \alpha =\frac{\gamma }{3}=\frac{1}{3}.\frac{\Delta V}{V\Delta t} $ $ \Rightarrow $ $ \alpha =\frac{1}{3}.\frac{0.15}{100\times 24} $ $ \Rightarrow $ $ \alpha =2\times {{10}^{-5}}/{{\,}^{o}}C $