Import Question JSON

Current Question (ID: 9709)

Question:

$\text{A man of mass 60 kg is standing on the ground and holding a string passing over a system of ideal pulleys. A mass of 10 kg is hanging over a light pulley such that the system is in equilibrium. The force exerted by the ground on the man is: (}g = \text{acceleration due to gravity)}$

Options:

1. $20g$
2. $45g$
3. $40g$
4. $60g$

Solution:

$\text{Hint: Apply Newton's law of motion.}$ $\text{Step 1: Apply Newton's third law on the block}$ $\text{For the 10 kg block in equilibrium:}$ $T = mg = 10g$ $\text{Step 2: Analyze the pulley system}$ $\text{From the diagram, we can see that the string passes over a movable pulley system. The tension in the string is T throughout.}$ $\text{The man experiences an upward force of 2T from the string (due to the pulley arrangement).}$ $\text{Step 3: Apply equilibrium condition for the man}$ $\text{For the man in equilibrium:}$ $N + 2T = mg$ $\text{Where N is the normal force from the ground on the man.}$ $\text{Substituting the values:}$ $N + 2(10g) = 60g$ $N = 60g - 20g = 40g$ $\text{Therefore, the force exerted by the ground on the man is } 40g\text{.}$

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
}