Import Question JSON

Current Question (ID: 8876)

Question:

$\text{If a ball is thrown vertically upwards with speed } u\text{, the distance covered during the last } t \text{ seconds of its ascent is:}$

Options:

1. $ut$
2. $\frac{1}{2}gt^2$
3. $ut - \frac{1}{2}gt^2$
4. $(u + gt)t$

Solution:

$\text{Hint: } S = ut + \frac{1}{2}at^2$ $\text{Step: Find the distance traveled.}$ $\text{Let the time of flight be } T \text{ then } T = \frac{u}{g}$ $\text{Let } h \text{ be the distance covered during the last 't' second of its ascent}$ $\text{Velocity at point B } = v_B = u - g(T - t) = u - g\left(\frac{u}{g} - t\right) = gt$ $\text{Using the kinematic equation for the motion from B to C:}$ $\Rightarrow h = v_B t - \frac{1}{2}gt^2 \Rightarrow h = gt^2 - \frac{1}{2}gt^2 = \frac{1}{2}gt^2$ $\text{Hence, option (2) is the correct answer.}$

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
}