If in the winter season, the surface temperature of the lake is $1°\mathrm{C}$, the temperature at the bottom of the lake will be:

1. $1°\mathrm{C}$

2. $0°\mathrm{C}$

3. $4°\mathrm{C}$

4. All values less than $1°\mathrm{C}$ are possible.

The readings of a bath on Celsius and Fahrenheit thermometers are in the ratio of 2: 5. The temperature of the bath is:

1. $-26.66°\mathrm{C}$

2. $40°\mathrm{C}$

3. $45.71°\mathrm{C}$

4. $26.66°\mathrm{C}$

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at $27.0°\mathrm{C}$. The diameter of the hole, when it is heated to 35.0 °C, is:

1. less than 4.24 cm.

2. equal to 4.24 cm.

3. more than 4.24 cm.

4. Data insufficient

On heating, a uniform metallic cylinder length increases by 3%. The area of cross-section of its base will increase by:

1. 1.5%

2. 3%

3. 9%

4. 6%

A circular metallic disc of radius R has a small circular cavity of radius r as shown in the figure. On heating the system,

1. R increases and r decreases.

2. R decreases and r increases.

3. Both R and r increases.

4. Both R and r decreases.

A uniform copper rod of length 50 cm and diameter 3.0 mm is kept on a frictionless horizontal surface at 20 °C. The coefficient of linear expansion of copper is $2.0\times {10}^{-5} {\mathrm{K}}^{-1}$ and Young's modulus is $1.2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$. The copper is heated to 100°C, then the tension developed in the copper rod is:

1. $12\times {10}^3 \mathrm{N}$

2. $36\times {10}^3 \mathrm{N}$

3. $18\times {10}^3 \mathrm{N}$

4. Zero

The coefficient of volume expansion of glycerin is $49\times {10}^{-5} {\mathrm{K}}^{-1}$. The fractional change in the density on a 30 °C rise in temperature is:

1. $1.47\times {10}^{-2}$

2. $1.47\times {10}^{-3}$

3. $1.47\times {10}^{-1}$

4. $1.47\times {10}^{-4}$

A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is $\mathrm{\alpha }$ and the coefficient of volume expansion of liquid is $\mathrm{\gamma }$. On increasing the temperature of (liquid + cube) system, the cube will sink if:

1. $\mathrm{\gamma }=3\mathrm{\alpha }$

2. $\mathrm{\gamma }>3\mathrm{\alpha }$

3. $\mathrm{\gamma }<3\mathrm{\alpha }$

4. $\mathrm{\gamma }=2\mathrm{\alpha }$

A steel tape is calibrated at 20°C. On a cold day when the temperature is -15°C, the percentage error in the tape will be: $\left[{\mathrm{\alpha }}_{\mathrm{steel}}=1.2\times {10}^{-5}°{\mathrm{C}}^{-1}\right]$

1. -0.035%

2. -0.042%

3. 0.012%

4. -0.018%

The water equivalent of 20 g of aluminium (specific heat 0.2 cal g^-1°C^-1) is:

1. 40 g

2. 4 g

3. 8 g

4. 160 g