$A$ 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:

To keep constant time,watches are fitted with a balance wheel made of:

$A$ uniform metal bar of length $10 \ m$ with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to a temperature rise of $40^{\circ} C$. If the coefficient of linear expansion of the metal is $2.5 \times 10^{-6} {}^{\circ} C^{-1}$,the maximum displacement of the midpoint of the bar is: (in $cm$)

When the temperature of a rod increases from $t$ to $(t + \Delta t)$,its moment of inertia increases from $I$ to $(I + \Delta I)$. If $\alpha$ is the coefficient of linear expansion of the rod,then the value of $(\frac{\Delta I}{I})$ is

At what temperature (in $ ^{\circ} C$) should a gold ring of diameter $6.230 \,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ (in $.7$)? Both diameters were measured at room temperature $(27^{\circ} C)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$)

$A$ steel tape $1 \; m$ long is correctly calibrated for a temperature of $27.0 \; ^{\circ}C$. The length of a steel rod measured by this tape is found to be $63.0 \; cm$ on a hot day when the temperature is $45.0 \; ^{\circ}C$. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is $27.0 \; ^{\circ}C$? (Coefficient of linear expansion of steel $\alpha = 1.20 \times 10^{-5} \; K^{-1}$)