The quantities of heat required to raise the temperature of two solid copper spheres of radii \(r_1\) and \(r_2\) \((r_1=1.5~r_2)\) through \(1~\text{K}\) are in the ratio:
1. \(\dfrac{9}{4}\)

2. \(\dfrac{3}{2}\)

3. \(\dfrac{5}{3}\)

4. \(\dfrac{27}{8}\)

Three stars A, B, C have surface temperatures ${\mathrm{T}}_{\mathrm{A}}$, ${\mathrm{T}}_{\mathrm{B}}$, ${\mathrm{T}}_{\mathrm{C}}$ respectively. Star A appears bluish, star B appears reddish and star C yellowish. Hence,

1. ${\mathrm{T}}_{\mathrm{A}}>{\mathrm{T}}_{\mathrm{B}}>{\mathrm{T}}_{\mathrm{C}}$

2. ${\mathrm{T}}_{\mathrm{B}}>{\mathrm{T}}_{\mathrm{C}}>{\mathrm{T}}_{\mathrm{A}}$

3. ${\mathrm{T}}_{\mathrm{C}}>{\mathrm{T}}_{\mathrm{B}}>{\mathrm{T}}_{\mathrm{A}}$

4. ${\mathrm{T}}_{\mathrm{A}}>{\mathrm{T}}_{\mathrm{C}}>{\mathrm{T}}_{\mathrm{B}}$

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 geyser heats water flowing at the rate of \(3.0\) liters per minute from \(27^\circ \text C\) to \(77^\circ \text C.\) If the geyser operates on a gas burner, what is the fuel consumption rate if its heat of combustion is \(4.0\times 10^4~\text{J/g}?\) 
1. \(15.7~\text g\) per min
2. \(15.10~\text g\) per min
3. \(14.39~\text g\) per min
4. \(17.11~\text g\) per min$\mathrm{}$

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. \(0.0111~\text{cm}\)

A brass wire \(1.8~\text m\) long at \(27^\circ \text C\) is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of \(-39^\circ \text C,\) what is the tension created in the wire?
( Assume diameter of the wire to be \(2.0~\text{mm}\) , coefficient of linear expansion of brass \(=2.0 \times10^{-5}~\text{K}^{-1},\) Young's modulus of brass\(=0.91 \times10^{11}~\text{Pa}\) )
1. \(3.8 \times 10^3~\text N\) 
2. \(3.8 \times 10^2~\text N\) 
3. \(2.9 \times 10^{-2}~\text N\) 
4. \(2.9 \times 10^{2}~\text N\)