A temperature of \(100^{\circ}\text {F}\) (Fahrenheit scale) is equal to \(T~\text{K}\) (Kelvin scale). The value of \(T\) is:
1. \(310.9\)
2. \(37.8\)
3. \(100\)
4. \(122.4\)

On a new scale of temperature, which is linear and called the \(\mathrm{W}\) scale, the freezing and boiling points of water are \(39^\circ ~\mathrm{W}\)$$and \(239^\circ ~\mathrm{W}\) respectively. What will be the temperature on the new scale corresponding to a temperature of \(39^\circ ~\mathrm{C}\) on the Celsius scale?
1. \(78^\circ ~\mathrm{C}\)
2. \(117^\circ ~\mathrm{W}\)
3. \(200^\circ ~\mathrm{W}\)
4. \(139^\circ ~\mathrm{W}\)

A pendulum clock runs faster by 5 seconds per day at \(20^{\circ}\mathrm {C}\) and goes slow by 10 second per day at \(35^{\circ}\mathrm {C}\). It shows the correct time at a temperature of:
1. \(27.5^{\circ}\mathrm {C}\)
2. \(25^{\circ}\mathrm {C}\)
3. \(30^{\circ}\mathrm {C}\)
4. \(33^{\circ}\mathrm {C}\)

A constrained steel rod of length \(l\), area of cross-section \(A\), Young's modulus \(Y\) and coefficient of linear expansion \(\alpha\)$$ is heated through \(t^{\circ}\text{C}\)$$. The work that can be performed by the rod when heated is:
1. \((YA\alpha t)(l\alpha t)\)
2. \(\frac{1}{2}(YA\alpha t)(l\alpha t)\)
3. \(\frac{1}{2}(YA\alpha t)\frac{1}{2}(l\alpha t)\)
4. \(2(YA\alpha t)(l\alpha t)\)

The coefficients of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\), lengths of brass and steel rods are \(l_1\) and \(l_2\) respectively. If (\(l_2-l_1\)) is maintained the same at all temperatures, Which one of the following relations holds good?
1. \(\alpha_1 l_2^2=\alpha_2l_1^2\)
2. \(\alpha_1^2 l_2=\alpha_2^2l_1\)
3. \(\alpha_1 l_1=\alpha_2l_2\)
4. \(\alpha_1 l_2=\alpha_2l_1\)

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. \(Y\alpha AL\Delta t\)

Two rods, one made of aluminium and the other made of steel, having initial lengths \(l_1\) and \(l_2\) are connected together to form a single rod of length $l_1+l_2$. The coefficient of linear expansion for aluminium and steel are ${\alpha }_a$ and ${\alpha }_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by \(t^\circ \mathrm{C},\) then the ratio \(\frac{l_1}{l_1+l_2}\) is:
1. $\frac{{\alpha }_s}{{\alpha }_a}$

2. $\frac{{\alpha }_a}{{\alpha }_s}$

3. $\frac{{\alpha }_a}{{\alpha }_a+{\alpha }_s}$

4. $\frac{{\alpha }_s}{{\alpha }_a+{\alpha }_s}$

If the same amount of heat is supplied to two spheres of the same material having the same radius (one is hollow and the other is solid), then:

The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.

What will be switched on when the bimetallic strip becomes hot?

The temperature of a wire of length \(1~\text{m}\) and an area of cross-section \(1~\text{cm}^2\) 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: \((\alpha = 10^{-5}/ ^{\circ} \mathrm {C} ~\text{and} ~Y = 10^{11} ~\text{N/m}^2)\)