The coefficients of linear expansion of brass and steel rods are α₁ and α₂, lengths of brass and steel rods are l₁ and l₂ respectively. If (l₂ - l₁) is maintained the same at all temperatures, Which one of the following relations holds good?

1. α₁l₂² = α₂l₁²

2. α₁²l₂ = α₂²l₁

3. α₁l₁ = α₂l₂

4. α₁l₂ = α₂l₁

A piece of ice falls from a height \(h\) so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice, and all energy of ice gets converted into heat during its fall. The value of \(h\) is: (Latent heat of ice is \(3.4\times10^5\) J/kg and \(g=10\) N/kg)

The two ends of a metal rod are maintained at temperatures \(100^{\circ}\mathrm{C}\) and \(110^{\circ}\mathrm{C}\). The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures \(200^{\circ}\mathrm{C}\) and \(210^{\circ}\mathrm{C}\), the rate of heat flow will be:
1. 44.0 J/s
2. 16.8 J/s
3. 8.0 J/s
4. 4.0 J/s

A certain quantity of water cools from \(70^{\circ}\mathrm{C}\) to \(60^{\circ}\mathrm{C}\) in the first 5 minutes and to \(54^{\circ}\mathrm{C}\) in the next 5 minutes. 
The temperature of the surroundings will be: 

The temperature of a wire of length 1 meter and an area of cross-section 1cm² is increased from \(0^{\circ} \mathrm {C}\) to \(100^{\circ} \mathrm {C}\). If the rod is not allowed to increase in length, the force required will be: \((\alpha = 10^{-5}/ ^{\circ} \mathrm {C} ~\text{and} ~Y = 10^{11} ~\text{N/m}^2)\)

A metal bar of length \(L\) and area of cross-section \(A\) is clamped between two rigid supports. For the material of the rod, its Young’s modulus is \(Y\) and the coefficient of linear expansion is \(\alpha\). If the temperature of the rod is increased by \(\Delta t^{\circ} \mathrm{C}\), the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then:

Mud houses are cooler in the summer and warmer in the winter because:

One likes to sit in the sunshine in the winter season, because:

Air is a bad conductor of heat or partly conducts heat. Still, a vacuum is to be placed between the walls of the thermos flask because: