Import Question JSON

Current Question (ID: 19154)

Question:

$\text{A monkey of mass } 50 \text{ kg climbs on a rope which can withstand the tension } (T) \text{ of } 350 \text{ N.}$ $\text{The monkey initially climbs down with an acceleration of } 4 \text{ m/s}^2 \text{ and then climbs up with an acceleration of } 5 \text{ m/s}^2.$ $\text{(take } g = 10 \text{ m/s}^2)$ $\text{Choose the correct option from the given ones:}$

Options:

1. $T = 700 \text{ N while climbing upward.}$
2. $T = 350 \text{ N while going downward.}$
3. $\text{The rope will break while the monkey climbs upward.}$
4. $\text{The rope will break while the monkey goes downward.}$

Solution:

$\text{Hint: } F_{\text{net}} = ma.$ $\text{Step 1: Find the tension in the rope when the monkey climbs down with acceleration } 4 \text{ m/s}^2.$ $mg - T = ma$ $\Rightarrow T = m(g - a) = 50(10 - 4)$ $\Rightarrow T = 300 \text{ N}$ $\text{So, the rope will not break.}$ $\text{Step 2: Find the tension in the rope when the monkey climbs up with acceleration } 5 \text{ m/s}^2.$ $T - mg = ma$ $\Rightarrow T = m(g + a) = 50(10 + 5)$ $\Rightarrow T = 750 \text{ N}$ $\text{So, the rope will break while the monkey climbs upward.}$ $\text{Hence, option (3) is the correct answer.}$

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
}