Import Question JSON

Current Question (ID: 9793)

Question:

$\text{A } 10 \text{ kg block is kept on a horizontal turntable that rotates at an angular velocity of } 2 \text{ rad/s. If the distance of the block from the center of the table is } 0.5 \text{ m, the net force on the block is:}$

Options:

1. $40 \text{ N}$
2. $20 \text{ N}$
3. $10 \text{ N}$
4. $\text{zero}$

Solution:

$\text{Hint: The net force on the block is equal to the centripetal force.}$ $\text{Step 1: Find the centripetal force on the object.}$ $F_C = m\omega^2 R$ $= 10 \times (2)^2 \times \frac{1}{2}$ $= 10 \times 4 \times 0.5 = 20 \text{ N}$

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
}