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Current Question (ID: 9747)

Question:

$\text{When a 5 kg plastic box is placed deep inside the water, it accelerates up at a rate of } \frac{g}{6}\text{. How much sand should be put inside the box so that it may accelerate down at the rate of } \frac{g}{6}\text{?}$

Options:

1. $2 \text{ kg}$
2. $3 \text{ kg}$
3. $4 \text{ kg}$
4. $5 \text{ kg}$

Solution:

$\text{Hint: } F = ma$ $\text{Step: Find the mass of the sand added to the box.}$ $\text{The initial equation of motion is given by;}$ $F_B - mg = ma$ $\Rightarrow F_B - mg = \frac{mg}{6} \ldots (1) \quad \left[a = \frac{g}{6}\right]$ $\text{Let the mass of sand added to the box is } m' \text{ kg}$ $\text{The new equation of motion is given by;}$ $(m + m')g - F_B = (m + m')a$ $\Rightarrow (m + m')g - F_B = \frac{(m+m')g}{6} \ldots (2) \quad \left[a = \frac{g}{6}\right]$ $\text{Adding equation (1) and (2) we get;}$ $m'g = \frac{(2m+m')g}{6}$ $\Rightarrow 6m' = 10 + m'$ $\Rightarrow 5m' = 10$ $\Rightarrow m' = 2 \text{ kg}$ $\text{Hence, option (1) is the correct answer.}$

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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
}