Import Question JSON

Current Question (ID: 9873)

Question:

$\text{The work done in increasing the length of a massless spring from its natural length 15 cm to 15.1 cm is 20 J. Work done in increasing the length from 15.1 cm to 15.2 cm will be:}$

Options:

1. $20 \text{ J}$
2. $40 \text{ J}$
3. $60 \text{ J}$
4. $80 \text{ J}$

Solution:

$\text{The elastic potential energy stored in a spring is given by the formula:}$ $U = \frac{1}{2}kx^2$ $\text{Where:}$ $\text{• } U \text{ is the elastic potential energy}$ $\text{• } k \text{ is the spring constant}$ $\text{• } x \text{ is the extension or compression of the spring from its equilibrium position.}$ $\text{Work done from 15 cm to 15.1 cm (extension 0.1 cm):}$ $W_1 = \frac{1}{2}k(0.1)^2 = 20 \text{ J}$ $\text{This gives us } k = \frac{2 \times 20}{(0.1)^2} = 4000 \text{ N/m}$ $\text{Total work done from 15 cm to 15.2 cm (extension 0.2 cm):}$ $W_{total} = \frac{1}{2}k(0.2)^2 = \frac{1}{2} \times 4000 \times (0.2)^2 = 80 \text{ J}$ $\text{Work done from 15.1 cm to 15.2 cm:}$ $W_2 = W_{total} - W_1 = 80 - 20 = 60 \text{ J}$ $\text{So, the correct answer is option 3.}$

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
}