Import Question JSON

Current Question (ID: 9856)

Question:

$\text{A body of mass 0.5 kg travels in a straight line with velocity } v = ax^{3/2} \text{ where } a = 5 \text{ m}^{-1/2} \text{s}^{-1}\text{. What is the work done by the net force during its displacement from } x = 0 \text{ to } x = 2 \text{ m?}$

Options:

1. $50 \text{ J}$
2. $45 \text{ J}$
3. $68 \text{ J}$
4. $90 \text{ J}$

Solution:

\text{Hint: Use the concept of the work-energy theorem.} \text{Step 1: Find the initial velocity of the body.} \text{Velocity is given by } v = ax^{3/2}, \text{ where } a = 5 \text{Initial velocity: } v_i = 5 \times (0)^{3/2} = 0 \text{Step 2: Find the final velocity of the body.} \text{Final velocity: } v_f = 5 \times (2)^{3/2} = 5 \times 2\sqrt{2} = 10\sqrt{2} \text{ m/s} \text{Step 3: Use the work-energy theorem.} \text{Work done by the net force:} W = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 W = \frac{1}{2}(0.5)(10\sqrt{2})^2 - 0 W = \frac{1}{2}(0.5)(200) = 50 \text{ J}

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
}