Import Question JSON

Current Question (ID: 10332)

Question:

$\text{A horizontal heavy uniform bar of weight } W \text{ is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to:}$

Options:

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

Solution:

\text{Let the mass of the rod be } M \\ \text{Weight } W = Mg \\ \text{Initially for equilibrium: } F + F = Mg \\ F = Mg/2 \\ \text{When one man withdraws, the torque on the rod:} \\ \tau = I \alpha = Mg \times l/2 \\ (Ml^2/3) \times \alpha = Mg \times l/2 \\ \text{Since } I = Ml^2/3 \\ \text{Angular acceleration: } \alpha = 3g/(2l) \\ \text{Linear acceleration: } a = (l/2) \times \alpha = 3g/4 \\ \text{If the new normal force at A is } F' \text{, then:} \\ Mg - F' = Ma \\ F' = Mg - Ma = Mg - 3Mg/4 = Mg/4 = W/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
}