Import Question JSON

Current Question (ID: 9886)

Question:

$\text{A body initially at rest and sliding along a frictionless track from a height } h \text{ (as shown in the figure) just completes a vertical circle of diameter } AB = D. \text{ The height } h \text{ is equal to:}$

Options:

1. $\frac{3}{2}D$
2. $D$
3. $\frac{7}{4}D$
4. $\frac{5}{4}D$

Solution:

$\text{Using conservation of energy:}$ $mgh = \frac{1}{2}mv^2 + mg \times 2R \text{ ......(i)}$ $\text{At point B, as the body just completes the circle:}$ $mg = \frac{mv^2}{R} \Rightarrow mv^2 = mgR \text{ .......(ii)}$ $\text{From equation (i):}$ $mgh = \frac{mgR}{2} + 2mgR = \frac{5mgR}{2}$ $h = \frac{5D}{4}$

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
}