Import Question JSON

Current Question (ID: 19401)

Question:

$\text{A uniform ring and uniform solid sphere roll down the same inclined plane at the same distance. If the ratio of their translational kinetic energies is } \frac{7}{x} \text{ then } x \text{ is: (Given mass and radius of the ring and sphere are equal)}$ $1. \ 10$ $2. \ 15$ $3. \ 20$ $4. \ 35$

Options:

1. $10$
2. $15$
3. $20$
4. $35$

Solution:

$\text{Hint: } a = \frac{g \sin \theta}{\left(1 + \frac{I}{mR^2}\right)}$ $K = \frac{1}{2} mv^2 = \frac{1}{2} m (2as)$ $\Rightarrow a_r = \frac{g \sin \theta}{2}$ $\Rightarrow a_s = \frac{5}{7} g \sin \theta$ $\frac{K_r}{K_s} = \frac{\frac{1}{2}}{\frac{5}{7}} = \frac{7}{10}$ $\therefore x = 10$

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
}