Import Question JSON

Current Question (ID: 9617)

Question:

$\text{A particle is thrown obliquely at } t = 0. \text{ The particle has the same K.E. at } t = 5 \text{ seconds and at } t = 9 \text{ seconds. The particle attains maximum altitude at:}$

Options:

1. $t = 6 \text{ s}$
2. $t = 7 \text{ s}$
3. $t = 8 \text{ s}$
4. $t = 14 \text{ s}$

Solution:

$\text{Hint: } H = \frac{u^2 \sin^2 \theta}{2g}$ $\text{Step: Find the time taken by the particle to attain the maximum altitude.}$ $\text{As the kinetic energy of the particle is the same at } t = 5 \text{ s and } t = 9 \text{ s, so the velocity in the vertical direction will be the same at the instances, but in the opposite direction.}$ $\text{So, } v_5 = -v_9$ $\Rightarrow u - 5g = -(u - 9g)$ $\Rightarrow 2u = 14g$ $\Rightarrow u = 7g$ $\text{At the maximum altitude: } v = 0$ $\Rightarrow 0 = 7g - gt$ $\Rightarrow t = 7 \text{ sec}$ $\text{Hence, option (2) is the correct answer.}$

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
}