Question

The volume of a metal sphere increases by $\text{0}\text{.15 }\\!\\!$ 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

Answer: (B)

$2.0\times {{10}^{-5}}/{{\,}^{o}}C$

Answer 2

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