Import Question JSON

Current Question (ID: 9728)

Question:

$\text{A parachutist falls downward with an acceleration of } 2 \text{ m/s}^2 \text{ at a height of } 200 \text{ m from the ground. Calculate the upthrust of air if the mass of the parachutist is } 60 \text{ kg: (assume } g = 10 \text{ m/s}^2\text{)}$

Options:

1. $480 \text{ N}$
2. $620 \text{ N}$
3. $720 \text{ N}$
4. $600 \text{ N}$

Solution:

$\text{Hint: } \vec{F}_{net} = m\vec{a}$ $\text{Step 1: Identify the forces acting on the parachutist.}$ $\text{There are two forces acting on the parachutist.}$ $\text{The first force is weight } mg \text{ acting vertically downward and the second force is air thrust } (F) \text{ acting vertically upward direction.}$ $\text{Step 2: Find the air upthrust force.}$ $\text{As the acceleration is vertically downward, so by applying Newton's law of motion, we get:}$ $\Rightarrow mg - F = ma$ $\Rightarrow F = m(g - a) = 60(10 - 2) = 60 \times 8 = 480 \text{ N}.$ $\text{Hence, option (1) is the correct answer.}$

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
}