Import Question JSON

Current Question (ID: 9616)

Question:

$\text{A particle } (A) \text{ is dropped from a height and another particle } (B) \text{ is projected in a horizontal direction with a speed of 5 m/s from the same height. The correct statement, from the following, is:}$

Options:

1. $\text{Particle } (A) \text{ will reach the ground first with respect to particle } (B).$
2. $\text{Particle } (B) \text{ will reach the ground first with respect to particle } (A).$
3. $\text{Both particles will reach the ground at the same time.}$
4. $\text{Both particles will reach the ground at the same speed.}$

Solution:

$\text{Hint: } s = ut + \frac{1}{2}at^2$ $\text{Step: Find the correct statement among the following.}$ $\text{The motion of both particles is shown in the figure below;}$ $\text{For particle (A)}$ $h = \frac{1}{2}gt^2$ $t_A = \sqrt{\frac{2h}{g}}$ $\text{For a particle (B) in the vertical direction}$ $\text{Uses } s = ut + \frac{1}{2}at^2$ $\Rightarrow h = \frac{1}{2}gt_B^2 \Rightarrow t_B = \sqrt{\frac{2h}{g}}$ $\text{Therefore, both particles will reach the ground at the same time.}$ $\text{Hence, option (3) is the correct answer.}$

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
}