Import Question JSON

Current Question (ID: 9846)

Question:

$\text{An object of mass } m = 1.5 \text{ kg is acted upon by the force as shown in the figure that varies with the position of the object as shown. If the object starts from rest at a point } x = 0, \text{ then what is its speed at } x = 50 \text{ m?}$

Options:

1. $20 \text{ m/s}$
2. $25 \text{ m/s}$
3. $15 \text{ m/s}$
4. $17 \text{ m/s}$

Solution:

$\text{(1) Work done by all the forces = } \Delta K$ $\text{Area under f - x graph = } \Delta K$ $\Rightarrow \frac{1}{2} \times (10 + 50) \times 10 = \frac{1}{2} \times 1.5 \times v^2$ $\Rightarrow 400 = v^2$ $\Rightarrow v = 20 \text{ m/s}$

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
}