Import Question JSON

Current Question (ID: 19258)

Question:

$\text{A body of mass } 0.5 \text{ kg travels on a straight line path with velocity } v = (3x^2 + 4) \text{ m/s. The net work done by the force during its displacement from } x = 0 \text{ to } x = 2 \text{ m is:}$ $1. \ 64 \text{ J}$ $2. \ 60 \text{ J}$ $3. \ 120 \text{ J}$ $4. \ 128 \text{ J}$

Options:

1. $64 \text{ J}$
2. $60 \text{ J}$
3. $120 \text{ J}$
4. $128 \text{ J}$

Solution:

$\text{Hint: Work done = change in kinetic energy.}$ $\text{Step: Find the net work done by the force.}$ $\text{According to the work-energy theorem, } W_{\text{net}} = K_{\text{Ef}} - K_{\text{Ei}}$ $\Rightarrow W_{\text{net}} = \frac{1}{2} mv_f^2 - \frac{1}{2} mv_i^2$ $\Rightarrow W_{\text{net}} = \frac{1}{2} \times 0.5 \times (16)^2 - \frac{1}{2} \times 0.5 \times (4)^2 \quad \left[ v_f = 3 \times (2)^2, \right]$ $\Rightarrow W_{\text{net}} = 64 - 4 = 60 \text{ J}$ $\text{Therefore, the net work done by the force is } 60 \text{ J}$ $\text{Hence, option (2) is the correct answer.}$

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
}