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

100 g of ice (latent heat 80 cal g^-1) at 0 °C is mixed with 100 g of water (specific heat 1 cal g^-1 °C^-1) at 80 °C. The final temperature of the mixture will be:

1. 0 °C

2. 40 °C

3. 80 °C

4. <0 °C

200 g of ice at -20°C is mixed with 500 g of water at 20°C in an insulating vessel. Final mass of water in vessel is: (Specific heat of ice$=0.5 \mathrm{cal} {\mathrm{g}}^{-1}°{\mathrm{C}}^{-1}$)

1. 700 g

2. 600 g

3. 400 g

4. 200 g

Which of the following material is most suitable for cooking utensils?

1. Low conductivity and low specific heat

2. High conductivity and low specific heat

3. Low conductivity and high specific heat

4. High conductivity and high specific heat