Import Question JSON

Current Question (ID: 9783)

Question:

$\text{Calculate the reading of the spring balance shown in the figure: (take } g = 10 \text{ m/s}^2\text{)}$ $\text{The system shows a 10 kg mass on a 30° inclined plane connected via a pulley to a 5 kg hanging mass, with the entire system accelerating upward at 2 m/s}^2$

Options:

1. $60 \text{ N}$
2. $40 \text{ N}$
3. $50 \text{ N}$
4. $80 \text{ N}$

Solution:

$\text{Hint: Tension in the string is the reading of spring balance.}$ $\text{Step 1: Draw the Free Body Diagram (FBD)}$ $\text{The system consists of a 10 kg mass on a 30° inclined plane connected to a 5 kg hanging mass via a pulley system.}$ $\text{Step 2: In the frame of the lift (accelerating reference frame):}$ $\text{Since the entire system is accelerating upward at 2 m/s}^2\text{, we need to consider pseudo force.}$ $\text{For the 5 kg block in the accelerating frame:}$ $g_{\text{eff}} = g + a = 10 + 2 = 12 \text{ m/s}^2$ $\text{Step 3: Reading of the spring balance:}$ $\text{The tension in the string (which is the spring balance reading) is:}$ $T = 5g' = 5 \times 12 = 60 \text{ N}$

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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
}