Import Question JSON

Current Question (ID: 9750)

Question:

$\text{A block of mass } M \text{ is pulled by a force } F\text{, making an angle } \theta \text{ with the horizontal on a smooth horizontal surface as shown. If } a \text{ is the acceleration of block on the surface, then the contact force between the block and the surface will be:}$

Options:

1. $Mg + Ma \cos \theta$
2. $Mg - Ma \cos \theta$
3. $Mg + Ma \tan \theta$
4. $Mg - Ma \tan \theta$

Solution:

$\text{Hint: Resolve the force F.}$ $\text{Step 1: Draw a free body diagram.}$ $\text{Step 2: Find the normal force.}$ $F\cos\theta = Ma$ $F = \frac{Ma}{\cos\theta} \ldots (1)$ $\text{Now,}$ $N + F\sin\theta = Mg$ $N = Mg - F\sin\theta$ $N = Mg - \frac{Ma}{\cos\theta} \times \sin\theta$ $N = Mg - Ma\tan\theta$

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
}