Import Question JSON

Current Question (ID: 9899)

Question:

$\text{A truck of mass 30,000 kg moves up an inclined plane of slope 1 in 100 }(\tan \theta = \frac{1}{100})\text{ at a speed of 30 km/h. The power of the truck is: (given }g = 10 \text{ ms}^{-2}\text{):}$

Options:

1. $25 \text{ kW}$
2. $10 \text{ kW}$
3. $5 \text{ kW}$
4. $2.5 \text{ kW}$

Solution:

$\text{Hint: The power of the truck is equal to the force on the truck multiplied by its velocity.}$ $\text{Step 1: Force on truck,}$ $F = mg\sin\theta$ $\text{Step 2: calculate }\theta$ $\tan \theta = \frac{1}{100} \approx \theta$ $\sin \theta \approx \theta \approx \tan \theta \text{ (}\theta\text{ is very small)}$ $\text{Step 3: Find the power using,}$ $P = F \cdot v$ $= (mg\sin\theta)v$ $= 3 \times 10^4 \times 10 \times \frac{1}{100} \times 30 \times \frac{5}{18}$ $= 25 \times 10^3 = 25 \text{ kW}$

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
}