Q. No.The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:
1. \(-40^\circ\)
2. \(40^\circ\)
3. \(0^\circ\)
4. \(50^\circ\)
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. \(139^\circ ~\mathrm{W}\)
| 1. | \(-415.44^\circ ~\text{F} ,-69.88^\circ ~\text{F}\) |
| 2. | \(-248.58^\circ ~\text{F} ,-56.60^\circ~ \text{F}\) |
| 3. | \(315.44^\circ ~\text{F} ,-69.88^\circ ~\text{F}\) |
| 4. | \(415.44^\circ ~\text{F} ,-79.88^\circ~ \text{F}\) |
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. \(80^\circ~\mathrm{C}\)
2. \(130^\circ~\mathrm{C}\)
3. \(160^\circ~\mathrm{C}\)
4. \(200^\circ~\mathrm{C}\)
1. \(L(1+\gamma\theta)\)
2. \(L(1+\frac\gamma2\theta)\)
3. \(L(1+\frac\gamma3\theta)\)
4. \(L(1+\frac{2\gamma}3\theta)\)
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. \(\alpha^2\)
1. \(3 \times 10^{-4} / ^\circ\text C\)
2. \(2 \times 10^{-4} / ^\circ\text C\)
3. \(6 \times 10^{-4} / ^\circ\text C\)
4. \(10^{-4} / ^\circ\text C\)
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:
1. \(\alpha_A\)
2. \(\frac{2\alpha_A}{6}\)
3. \(\frac{4\alpha_A}{6}\)
4. \(\frac{5\alpha_A}{6}\)
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 a wire with a diameter of \(2.0~\text{mm}?\)
(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. \(2.9 \times 10^{2}~\text N\)
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