Question

A circular metallic ring of radius R has a small gap of width d. The coefficient of thermal expansion of the metal is $\alpha$ in appropriate units. If we increase the temperature of the ring by an amount $\Delta T$, then width of the gap.

• A. Will increase by an amount $d\alpha \Delta T$
• B. Will not change
• C. Will increase by an amount $(2\pi R-d)\alpha \Delta T$
• D. Will decrease by an amount $d\alpha \Delta T$

Answer 1

Answer: (A)

Will increase by an amount $d\alpha \Delta T$

The total circumference is $2\pi R-d$

Change in length=$(2\pi R-d)\alpha \delta T$

So change in the gap width is $d\alpha \delta T$