Import Question JSON

Current Question (ID: 19260)

Question:

$\text{Sand is being dropped from a stationary dropper at a rate of } 0.5 \text{ kgs}^{-1}$ $\text{on a conveyor belt moving with a velocity of } 5 \text{ ms}^{-1}. \text{ The power needed to keep the belt moving with the same velocity will be:}$

Options:

1. $1.25 \text{ W}$
2. $2.5 \text{ W}$
3. $6.25 \text{ W}$
4. $12.5 \text{ W}$

Solution:

$\text{Hint: } F = \frac{d(mv)}{dt}$ $\text{Step: Find the power needed to keep the belt moving.}$ $P = \frac{dK}{dt} = \frac{d}{dt} \left( \frac{1}{2} mv^2 \right) \Rightarrow \frac{v^2}{2} \cdot \frac{dm}{dt}$ $P = \frac{5^2}{2} \times 0.5 = 6.25 \text{ W}$

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
}