The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:

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. $139^\circ ~\text{W}$

The ice-point reading on a thermometer scale is found to be $20^\circ,$ while the steam point is found to be $70^\circ.$ When this thermometer reads $100^\circ ,$ the actual temperature is:
1. $80^\circ\text{C}$
2. $130^\circ\text{C}$
3. $160^\circ\text{C}$
4. $200^\circ\text{C}$

The coefficient 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 $(L_2-L_1)$ remains the same at all temperatures, which one of the following relations holds good?
1. $\alpha_1L_2^2=\alpha_2L_1^2$
2. $\alpha_1^2L_2=\alpha_2^2L_1$
3. $\alpha_1L_1=\alpha_2L_2$
4. $\alpha_1L_2=\alpha_2L_1$

The coefficient of area expansion $\beta$ of a rectangular sheet of a solid in terms of the coefficient of linear expansion $\alpha$ is:
1. $2\alpha$
2. $\alpha$
3. $3\alpha$
4. $\alpha^2$

A rod $\mathrm{A}$ has a coefficient of thermal expansion $(\alpha_A)$ which is twice of that of rod $\mathrm{B}$ $(\alpha_B)$. The two rods have length $l_A,~l_B$ where $l_A=2l_B$. If the two rods were joined end-to-end, the average coefficient of thermal expansion is:

A brass wire $1.8~\text m$ long at $27^\circ \text C$ is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of $-39^\circ \text C,$ what is the tension created in the wire?
( Assume diameter of the wire to be $2.0~\text{mm}$ , coefficient of linear expansion of brass $=2.0 \times10^{-5}~\text{K}^{-1},$ Young's modulus of brass$=0.91 \times10^{11}~\text{Pa}$ )
1. $3.8 \times 10^3~\text N$ 
2. $3.8 \times 10^2~\text N$ 
3. $2.9 \times 10^{-2}~\text N$ 
4. $2.9 \times 10^{2}~\text N$