Question

The volume of a metal sphere increase by $0.15\%$ when its temperature is raised by ${24}^{o}C$. 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 $2.0\times {10}^{-5}{/}^{o}C$

If initial volume is $V$ and chnage in volume is $\Delta V$ then

$\Delta V=V\gamma \Delta t$ ...................(1)

Volume coefficient $\gamma$ is $3\alpha$, where $\alpha$ is linear expansion coefficient so $\Delta V=V3\alpha \Delta t$

Given that $\Delta V=V\times 0.15/100=.0015V$

Putting above values with $\Delta t={24}^{0}C$ in equation 1

we get $\alpha =2.0\times {10}^{-5}{/}^{0}C$

Option B is correct.