Import Question JSON

Current Question (ID: 19994)

Question:

$\text{A heavy ball of mass } M \text{ is suspended from the ceiling of a car by a light string of mass } m (m << M).$ $\text{When the car is at rest, the speed of transverse waves in the string is } 60 \text{ ms}^{-1}.$ $\text{When the car has acceleration } a, \text{ the wave speed increases to } 60.5 \text{ ms}^{-1}.$ $\text{The value of } a, \text{ in terms of gravitational acceleration } g \text{ is closest to:}$

Options:

1. $\frac{g}{\sqrt{30}}$
2. $\frac{g}{\sqrt{5}}$
3. $\frac{g}{10}$
4. $\frac{g}{20}$

Solution:

$\text{Hint: } v = \sqrt{\frac{T}{\mu}}$

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
}