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Q. No.The moment of inertia of a metallic rod of length \(L,\) about an axis passing through its centre-of-mass and perpendicular to the rod, is \(I_0.\) When the temperature is raised by \(\Delta\theta,\) it increases by \(\Delta I_0. \) The coefficient of linear expansion of the rod's material is:
1.
\(\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\)
2.
\(\dfrac12\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\)
3.
\(\dfrac15\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\)
4.
\(2\left(\dfrac{\Delta I_0}{I_0}\right)\dfrac{1}{\Delta\theta}\)
Subtopic: Ā Thermal Expansion |
Ā 63%
Level 2: 60%+
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Two bodies \(A,B\) are maintained at temperatures \(\theta_A=100^\circ\text C\) and \(\theta_B=0^\circ\text C.\) Two thermally conducting rods \((P,~Q)\) of different conductivities and of different dimensions are connected between \(A\) and \(B.\) The conductivity of \(P\) is twice that of \(Q.\) The sides of the rods are insulated. If the mid-points of the two rods are connected to each other by a thin conducting wire (after equilibrium is reached),
| 1. | heat would flow from \(P\) to \(Q\). |
| 2. | heat would flow from \(Q\) to \(P\). |
| 3. | no flow of heat occurs between \(P\) & \(Q\). |
| 4. | flow of heat may occur back and forth between \(P\) & \(Q,\) varying with time. |
Subtopic: Ā Conduction |
Ā 51%
Level 3: 35%-60%
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A body cools from \(52^\circ \text{C}\) to \(48^\circ \text{C}\) in \(6\) minutes. How much time will the same body take to cool from \(53^\circ \text{C}\) to \(47^\circ \text{C}?\) Assume cooling is linear with time.
1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
Subtopic: Ā Newton's Law of Cooling |
Ā 82%
Level 1: 80%+
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A vessel containing water is heated from the top by means of a heater, just above the water surface. Assume that the temperature of the water was just above \(0^\circ\text{C},\) in the beginning. The temperature \((\theta_A)\) at the bottom is measured as a function of time. Which of the following shows the correct plot?
| 1. | \(a\) | 2. | \(b\) |
| 3. | \(c\) | 4. | \(d\) |
Subtopic: Ā Convection |
Ā 51%
Level 3: 35%-60%
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Blackbody radiation emerging from a body at an absolute temperate \(T\) is allowed to fall on an ideal gas enclosed in a transparent vessel until its temperature reaches a steady state value of \(T_1.\) Then:
1. \(T_1=T\)
2. \(T_1>T\)
3. \(T_1<T\)
4. any of the above may be true.
1. \(T_1=T\)
2. \(T_1>T\)
3. \(T_1<T\)
4. any of the above may be true.
Subtopic: Ā Stefan-Boltzmann Law |
Ā 54%
Level 3: 35%-60%
Hints
A solid non-expanding tank contains air (at atm pressure \({\large p}_0~\&~0^{\circ}\text{C}\)) and mercury, the mercury filling half the tank. Let coefficient of expansion of mercury be \({\Large\gamma}_L.\) If the temperature is raised by \(\theta\) (a few degree Celsius) the pressure of air increases by (nearly):
1. \({\Large\gamma}_L\theta\times{\large p}_0 ~\)
2. \({\Large\frac{\theta}{273}}{\large p}_0\)
3. \({\dfrac{{\Large\gamma}_L\theta}{273}}{\large p}_0\)
4. \(\Big({\Large\gamma}_L\theta+{\Large\frac{\theta}{273}}\Big){\large p}_0 \)
1. \({\Large\gamma}_L\theta\times{\large p}_0 ~\)
2. \({\Large\frac{\theta}{273}}{\large p}_0\)
3. \({\dfrac{{\Large\gamma}_L\theta}{273}}{\large p}_0\)
4. \(\Big({\Large\gamma}_L\theta+{\Large\frac{\theta}{273}}\Big){\large p}_0 \)
Subtopic: Ā Thermal Expansion |
Level 3: 35%-60%
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The radiation emerging from a furnace (blackbody) is found to have a most probable wavelength \(\lambda_m\) and the gas molecules (air) emerging from it have an RMS speed \(v.\) As the temperature of the furnace is varied:
| 1. | \(\lambda_m\propto v \) | 2. | \(\lambda_m\propto \dfrac1v \) |
| 3. | \(\lambda_m\propto v^2 \) | 4. | \(\lambda_m\propto \dfrac1{v^2} \) |
Subtopic: Ā Wien's Displacement Law |
Ā 65%
Level 2: 60%+
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A body loses heat at a rate of \(2~\text{W/min}\) when it is at a temperature of \(40^{\circ}\text C,\) but at a rate of \(1~\text{W/min}\) when its temperature is \(30^{\circ}\text C.\) The temperature of the surroundings is:
1. \(25^{\circ}\text{C}\)
2. \(20^{\circ}\text{C}\)
3. \(10^{\circ}\text C\)
4. \(35^{\circ}\text C\)
1. \(25^{\circ}\text{C}\)
2. \(20^{\circ}\text{C}\)
3. \(10^{\circ}\text C\)
4. \(35^{\circ}\text C\)
Subtopic: Ā Newton's Law of Cooling |
Ā 70%
Level 2: 60%+
Hints
Ice (\(0^{\circ}\text{C}\)) is kept in an insulated reservoir with an opening that is covered at the top with a cloth. When a black cloth \((B)\) is placed at the top, the ice melts at \(\dfrac{2}{3}~\text {gram/min}.\) When an ordinary cloth \((G)\) is placed, the rate of melting is \(\dfrac{2}{5}~\text {gram/min}.\) The emissivity of \(G\) is: (assuming that \(B\) behaves as a blackbody)
| 1. | \(0.6\) | 2. | \(0.3\) |
| 3. | \(0.4\) | 4. | \(0.5\) |
Subtopic: Ā Stefan-Boltzmann Law |
Ā 71%
Level 2: 60%+
Hints
A piece of iron of water equivalent \(10 \) g is taken from a furnace and put into a calorimeter containing \(100\) g of water at an initial temperature of \(20^{\circ} \text{C}.\) The final temperature of the system is observed to be \(80^{\circ} \text{C}.\) Ignore the thermal capacity of the calorimeter and any loss of heat. The temperature of the furnace is:
1. \(600^{\circ} \text{C}\)
2. \(620^{\circ} \text{C}\)
3. \(680^{\circ} \text{C}\)
4. \(520^{\circ} \text{C}\)
1. \(600^{\circ} \text{C}\)
2. \(620^{\circ} \text{C}\)
3. \(680^{\circ} \text{C}\)
4. \(520^{\circ} \text{C}\)
Subtopic: Ā Calorimetry |
Ā 63%
Level 2: 60%+
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