Import Question JSON

Current Question (ID: 10290)

Question:

$\text{A uniform cubical block of side L rests on a rough horizontal surface with coefficient of friction } \mu. \text{ A horizontal force F is applied on the block as shown. If there is sufficient friction between the block and the ground, then the torque due to normal reaction about its centre of mass is:}$

Options:

1. $\text{Zero}$
2. $FL$
3. $\frac{FL}{2}$
4. $\frac{3FL}{2}$

Solution:

$\text{Hint: Torque due to force F and frictional force will be balanced by that due to the normal reaction.}$ $\text{Step 1: Balance the force along the horizontal direction.}$ $f = F$ $\text{Step 2: Balancing the torque about the centre of mass.}$ $F \times \frac{L}{2} + F \times \frac{L}{2} = \tau_N$ $\tau_N = FL = \text{torque due to normal reaction.}$

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
}