Import Question JSON

Current Question (ID: 9871)

Question:

$\text{A vertical spring with a force constant } k \text{ is fixed on a table. A ball of mass } m \text{ at a height } h \text{ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance } d. \text{ The net work done in the process is:}$

Options:

1. $mg(h + d) + \frac{1}{2}kd^2$
2. $mg(h + d) - \frac{1}{2}kd^2$
3. $mg(h - d) - \frac{1}{2}kd^2$
4. $mg(h - d) + \frac{1}{2}kd^2$

Solution:

$\text{Given:}$ $\text{Force constant of spring = } k$ $\text{Mass of the ball = } m$ $\text{Height from which ball is released = } h$ $\text{Compression of spring = } d$ $\text{Work done is equal to change in energy of body.}$ $\text{The situation is shown in figure. When mass } m \text{ falls vertically on spring, then spring is compressed by distance } d.$ $\text{Hence, net work done in the process is,}$ $W = \text{Potential energy stored in the spring + Loss of potential energy of mass}$ $= mg(h + d) - \frac{1}{2}kd^2$

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
}