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Current Question (ID: 9742)

Question:

$\text{In the given figure, spring balance is massless, so the reading of spring balance will be:}$

Options:

1. $2\text{ kg}$
2. $3.5\text{ kg}$
3. $2.9\text{ kg}$
4. $3.1\text{ kg}$

Solution:

\text{Hint: Spring balance measures tension.} \text{Step 1: Replace spring with wire} \text{The spring balance can be replaced with a wire, and the system becomes a pulley system with masses 5 kg and 2 kg.} \text{Step 2: Solve for pulley system} \text{For a pulley system with masses } m_1 \text{ and } m_2\text{, the tension is:} T = \frac{2 \times m_1 \times m_2}{m_1 + m_2} \times g \text{For the 5 kg mass: } 5g - T = 5a \text{For the 2 kg mass: } T - 2g = 2a \text{Solving: } T = \frac{20g}{7} \text{Reading} = \frac{T}{g} = \frac{20}{7} = 2.9\text{ kg} \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
}