Import Question JSON

Current Question (ID: 8726)

Question:

$\text{If the units of force and length, are increased by four times, then the unit of energy increases by:}$

Options:

1. $16 \text{ times}$
2. $8 \text{ times}$
3. $2 \text{ times}$
4. $4 \text{ times}$

Solution:

$\text{Hint: } E = W = F \cdot s$ $\text{Step: Find the increase in the unit of energy.}$ $\text{The energy of the particle in terms of } F \text{ and } L \text{ is given by;}$ $E = F \cdot L$ $\text{Now, if each unit are increased by 4 times then the new unit of energy} = (4 \times \text{N})(4 \times \text{m}) = 16 \text{Nm}$ $\text{Therefore, energy increases by 16 times if the force and length increase by 4 times.}$ $\text{Hence, option (1) is the correct answer.}$

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
}