Import Question JSON

Current Question (ID: 19230)

Question:

$\text{A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled } 3 \text{ m is:}$

Options:

1. $2.5 \text{ J}$
2. $6.5 \text{ J}$
3. $4 \text{ J}$
4. $5 \text{ J}$

Solution:

$\text{Hint: Work done = change in } K.E.$ $\text{Step 1: Find the work done till } x = 3 \text{ m.}$ $\text{The work done is given by the area under } F-x \text{ graph.}$ $W = 2 \times 2 + \frac{1}{2} [2 + 3] \times 1$ $\Rightarrow W = 6.5 \text{ J}$ $\text{Step 2: Find the final kinetic energy of the particle.}$ $\text{By using the work-energy theorem, we get;}$ $W = \Delta K$ $\Rightarrow W = K.E_f - K.E_i$ $\Rightarrow W = K.E_f \Rightarrow K.E_f = 6.5 \text{ J} \quad [K.E_i = 0]$ $\text{Hence, option (2) is the correct answer.}$

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
}