Import Question JSON

Current Question (ID: 19306)

Question:

$\text{A variable force given by;} \ F = 5kx \ \text{(in newtons) acts on a body moving along the} \ x\text{-axis, where} \ k \ \text{is a constant.}$ $\text{What is the work done by this force as the body moves from} \ x = 2 \ m \ \text{to} \ x = 5 \ m?$

Options:

1. $\left( \frac{205}{2} k \right) \ \text{J}$
2. $\left( \frac{105}{2} k \right) \ \text{J}$
3. $(52k) \ \text{J}$
4. $(51k) \ \text{J}$

Solution:

$\text{Hint:} \ W = \int F \cdot dx.$ $\text{Step: Find the work done by the force in displacing the body from} \ x = 2 \ m \ \text{to} \ x = 5 \ m.$ $W = \int_{x=2}^{x=5} F dx = \int_{x=2}^{x=5} (5kx) dx$ $\Rightarrow W = \frac{5k}{2} \left[ x^2 \right]_2^5 = \frac{5k}{2} \left[ 5^2 - 2^2 \right]$ $\Rightarrow W = \left( \frac{105k}{2} \right).$ $\text{Hence, option (2) is the correct answer.}$

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
}