Import Question JSON

Current Question (ID: 10768)

Question:

$\text{Two rods of the same length and the same area of the cross-section are joined. The temperature of the two ends is shown in the figure.}$ $\text{As we move along the rod, temperature varies as shown in the following figure.}$ $\text{Then:}$

Options:

1. $K_1 > K_2$ (Correct)
2. $K_1 = K_2$
3. $K_1 < K_2$
4. $\text{none of these}$

Solution:

$\text{Hint: Conduction current through both rods is the same.}$ $\text{Step: Find the relation between } K_1 \text{ and } K_2.$ $\text{Conduction current through the rod is given by;}$ $i = \frac{dQ}{dt} = kA\left(\frac{dT}{dx}\right)$ $\text{The conduction current through both rods is the same since both are connected in a series combination i.e., } K \times \frac{dT}{dx} = \text{constant}$ $\Rightarrow \frac{dT}{dx} \propto \frac{1}{K}$ $\text{From the graph given below;}$ $\text{The slope for the second rod is more than the first rod i.e., } \theta_2 > \theta_1$ $\Rightarrow \tan \theta_2 > \tan \theta_1$ $\Rightarrow \left(\frac{dT}{dx}\right)_2 > \left(\frac{dT}{dx}\right)_1$ $\Rightarrow K_1 > K_2 \left[\frac{dT}{dx} \propto \frac{1}{K}\right]$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}