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