Question

The radius of a ring is R and its coefficient of linear expansion is $\alpha$. If the temperature ring increases by $\theta$ then its Circumference will increase by

• A. $\pi R^2\alpha \theta$
• B. $2\pi R\alpha \theta$
• C. $\pi R\alpha \frac{\theta }{2}$
• D. $\pi R\alpha \frac{\theta }{4}$

Answer 1

The correct option is B $2\pi R\alpha \theta$

We know$,$

$L=2\pi r$

$\frac{\Delta L}{L}=\alpha \Delta T$

$\Delta L=L\alpha \Delta T$

$=2\pi r\alpha \Delta T=2\pi r\alpha \theta$ $(\because \Delta T=\theta )$
Hence,

option $\left(B\right)$ is correct answer.