Import Question JSON

Current Question (ID: 10286)

Question:

$\text{A meter stick is balanced on a knife edge at its center. When two coins, each of the mass 5 gm are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the meter stick?}$

Options:

1. $66 \text{ gm}$
2. $56 \text{ gm}$
3. $76 \text{ gm}$
4. $79 \text{ gm}$

Solution:

$\text{Hint: Apply the concept of rotational equilibrium.}$ $\text{Step: Balance the torque about the point of equilibrium.}$ $\text{Mass of meter stick} = m'$ $\text{The mass of each coin} = 5 \text{ g}$ $\text{Total mass of two coins} = 10 \text{ g}$ $\tau_N = \tau_W$ $\text{we know that } \tau = r \times F$ $\text{For rotational equilibrium, clockwise torque = counterclockwise torque}$ $\text{Torque due to coins about 45 cm mark} = \text{Torque due to meter stick about 45 cm mark}$ $10g \times (45 - 12) = m'g \times (50 - 45)$ $10g \times 33 = m'g \times 5$ $330g = 5m'g$ $m' = \frac{330}{5} = 66 \text{ gm}$ $\text{Hence, option (1) is the correct answer.}$

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
}