Import Question JSON

Current Question (ID: 9843)

Question:

$\text{A force of 5 N making an angle } \theta \text{ with the horizontal acting on an object displaces it by 0.4 m along the horizontal direction. If the object gains kinetic energy of 1 J then the component of the force is:}$

Options:

1. $\text{1.5 N}$
2. $\text{2.5 N}$
3. $\text{3.5 N}$
4. $\text{4.5 N}$

Solution:

$\text{Hint: Apply the work energy theorem.}$ $\text{Step 1: Find the work done by the external force.}$ $\text{Since the object is moving horizontally, the work done by the vertical component of force is zero.}$ $\text{Work done by the horizontal component of force = } F_x (0.4)$ $\text{Step 2: Find the horizontal component of force acting on the particle.}$ $\text{Apply work energy theorem.}$ $F_x (0.4) = 1 \text{ J}$ $F_x = 2.5 \text{ N}$

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
}