Import Question JSON

Current Question (ID: 19197)

Question:

$\text{A block of mass } M \text{ placed inside a box descends vertically with acceleration } 'a'.$ $\text{The block exerts a force equal to one-fourth of its weight on the floor of the box.}$ $\text{The value of } 'a' \text{ will be:}$

Options:

1. $\frac{g}{4}$
2. $\frac{2g}{3}$
3. $\frac{3g}{4}$
4. $g$

Solution:

$\text{Let the normal force exerted by the block on the floor be } N.$ $\text{Given, } N = \frac{1}{4}Mg.$ $\text{Using the equation of motion:}$ $Mg - N = Ma$ $\Rightarrow Mg - \frac{1}{4}Mg = Ma$ $\Rightarrow \frac{3}{4}Mg = Ma$ $\Rightarrow a = \frac{3g}{4}$

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
}