Import Question JSON

Current Question (ID: 19039)

Question:

$\text{A juggler throws balls vertically upward with the same initial speed.}$ $\text{He throws } n \text{ balls per second. If he throws the next ball just as the}$ $\text{previous one reaches its maximum height, what is the maximum}$ $\text{height which each ball will reach?}$

Options:

1. $\frac{g}{2n}$
2. $\frac{g}{n}$
3. $2gn$
4. $\frac{g}{2n^2}$

Solution:

$\text{Hint: } H = \frac{u^2}{2g}$ $\text{Step 1: Find the time to reach maximum height.}$ $0 = u - gt$ $\Rightarrow t = \frac{u}{g}$ $\text{Step 2: Find the value of } u \text{ in terms of } n.$ $\text{The juggler throws the next ball exactly when the first reaches the}$ $\text{top. Hence, the time between throws is:}$ $t = \frac{u}{g} = \frac{1}{n}$ $\Rightarrow u = \frac{g}{n}$ $\text{Step 3: Find the maximum height.}$ $H = \frac{u^2}{2g}$ $\Rightarrow H = \frac{(g/n)^2}{2g}$ $\Rightarrow H = \frac{g}{2n^2}$ $\text{Hence, option (4) is the correct answer.}$

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
}