A steel tape \(1\) m long is correctly calibrated for a temperature of \(27^\circ \text{C}\). 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 \(45^\circ \text{C}\). What is the actual length of the steel rod on that day?
(Coefficient of linear expansion of steel = \(1.20\times 10^{-5}~\text{K}^{-1}\)).
1. \( 62.485 \) cm
2. \( 60.762 \) cm
3. \( 65.935 \) cm
4. \( 63.013\) cm

A large steel wheel is to be fitted onto a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the wheel's central hole has a diameter of 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft?
(Assume the coefficient of linear expansion of the steel to be constant over the required temperature range  and \(\alpha\) steel = \(1.20 \times 10^{-5} K^{-1}\))
1. 68°C
2. -70°C
3.  -69°C
4. -67°C

A hole is drilled in a copper sheet. The diameter of the hole is \(4.24~\text{cm}\) at \(27.0^\circ \text C.\) What is the change in the diameter of the hole when the sheet is heated to \(227^\circ \text C?\)
(the coefficient of linear expansion of copper \(\alpha=1.70\times 10^{-5}~\text K^{-1}\))
1. \(0.0144~\text{cm}\)
2. \(0.0234~\text{cm}\)
3. \(0.0123~\text{cm}\)
4. \(0.0111~\text{cm}\)

The coefficient of volume expansion of glycerine is \(49\times 10^{-5}~\text {K}^{-1}.\) What is the fractional change in its density for a \(30^\circ \text{C}\) rise in temperature?
1. \(1.44\times10^{-3}\)
2. \(1.57\times10^{-3}\)
3. \(1.57\times10^{-2}\)
4. \(1.44\times10^{-2}\)