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Three rods of identical dimensions but made of materials of conductivities \(K,~2K,~K\) are connected in series. The two ends \(A~,B\) are maintained at temperatures of \(0^{\circ} \text{C},~100^{\circ} \text{C}\) respectively. Assume no loss of heat from the sides. The temperatures of the junctions \(X,~Y\) are:
1. \(25^\circ\text C,~75^\circ\text C\)
2. \(40^\circ\text C,~60^\circ\text C\)
3. \(20^\circ\text C,~80^\circ\text C\)
4. \(30^\circ\text C,~70^\circ\text C\)
1. \(25^\circ\text C,~75^\circ\text C\)
2. \(40^\circ\text C,~60^\circ\text C\)
3. \(20^\circ\text C,~80^\circ\text C\)
4. \(30^\circ\text C,~70^\circ\text C\)
Subtopic: Â Conduction |
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Level 2: 60%+
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If the ends of the meter stick are maintained at \(\theta_1\)\(^\circ \text{C}\) and \(\theta_2\)\(^\circ \text{C},\) the temperatures measured at the \(25\) cm and \(80\) cm marks are observed to be \(35^\circ \text{C}\) and \(68^\circ \text{C}\) respectively. Then the temperatures of the left end
(\(\theta_1\)\(^\circ \text{C}\)) and the right end (\(\theta_2\)\(^\circ \text{C}\)) are:
(\(\theta_1\)\(^\circ \text{C}\)) and the right end (\(\theta_2\)\(^\circ \text{C}\)) are:
| 1. | \(\theta_{1}=0, ~\theta_{2}=90\) |
| 2. | \(\theta_{1}=10,~\theta_{2}=85\) |
| 3. | \(\theta_{1}=20, ~\theta_{2}=80\) |
| 4. | \(\theta_{1}=30, ~\theta_{2}=100\) |
Subtopic: Â Conduction |
 70%
Level 2: 60%+
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Two rods of identical dimensions are joined end-to-end, and the ends of the composite rod are kept at \(0^\circ\text{C}\) and \(100^\circ\text{C}\) (as shown in the diagram). The temperature of the joint is found to be \(40^\circ\text{C}.\) Assuming no loss of heat through the sides of the rods, the ratio of the conductivities of the rods \(\dfrac{K_1}{K_2}\) is:
| 1. | \(\dfrac32\) | 2. | \(\dfrac23\) |
| 3. | \(\dfrac11\) | 4. | \(\dfrac{\sqrt3}{\sqrt2}\) |
Subtopic: Â Conduction |
 80%
Level 1: 80%+
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Two rods \(A\) and \(B\) of different materials are welded together as shown in the figure. Their thermal conductivities are \(K_1\) and \(K_2.\) The thermal conductivity of the composite rod will be:
| 1. | \(\dfrac{3(K_1+K_2)}{2}\) | 2. | \(K_1+K_2\) |
| 3. | \(2(K_1+K_2)\) | 4. | \(\dfrac{(K_1+K_2)}{2}\) |
Subtopic: Â Conduction |
 76%
Level 2: 60%+
NEET - 2017
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