Import Question JSON

Current Question (ID: 19314)

Question:

$\text{A mass } m \text{ is supported by a massless string wound around a uniform hollow cylinder of mass } m \text{ and radius } R. \text{ If the string does not slip on the cylinder, with what acceleration will the mass fall on release?}$

Options:

1. $\frac{g}{2}$
2. $\frac{5g}{6}$
3. $g$
4. $\frac{2g}{3}$

Solution:

$\text{Hint: write Newton's laws for translatory and rotatory motion.}$ $\text{For translatory motion of block:}$ $mg - T = ma \quad \text{(i)}$ $\text{For cylinder:}$ $\tau = TR = I \alpha$ $TR = \left(mR^2\right) \frac{a}{R} \quad \text{or} \quad T = ma$ $\text{By adding equation (i) and (iii):}$ $mg = 2ma \quad \Rightarrow \quad a = \frac{g}{2}$

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
}