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

If a graph is plotted between the temperature of a body in degrees Celsius (along the $\mathrm{y}$-axis) and Fahrenheit (along the $\mathrm{x}$-axis) at different temperatures, then the slope of the graph will be:
1. $\frac{5}{9}$

2. $\frac{9}{5}$

3. $\frac{3}{5}$

4. $\frac{5}{3}$

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. $122.4$

The temperature of a body on the Kelvin scale is found to be $x^\circ~\text K.$ When it is measured by a Fahrenheit thermometer, it is found to be $x^\circ~\text F,$ then the value of $x$ is:
1. $40$
2. $313$
3. $574.25$
4. $301.25$

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. $\alpha_1 l_2=\alpha_2l_1$

The value of the coefficient of volume expansion of glycerin is $5\times10^{-4}$ K^-1. The fractional change in the density of glycerin for a temperature increase of $40^\circ \mathrm{C}$ will be:

A copper rod of $88$ cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is:
$\left(\alpha_{Cu}= 1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}= 2.2\times10^{-5}~\text{K}^{-1}\right)$
1. $68~\text{cm}$
2. $6.8~\text{cm}$
3. $113.9~\text{cm}$
4. $88~\text{cm}$

When a uniform rod is heated, which of its following properties will increase as a result of it?
1. mass
2. weight
3. center of mass
4. moment of inertia