Import Question JSON

Current Question (ID: 19479)

Question:

$\text{A particle is released from a height equal to radius of earth, } R. \text{ Its velocity when it strikes the ground is:}$

Options:

1. $\sqrt{gR}$
2. $\sqrt{\frac{gR}{2}}$
3. $\sqrt{2gR}$
4. $\sqrt{4gR}$

Solution:

$\text{Hint: Conserve mechanical energy.}$ $\text{Step: Calculate the velocity of the particle when it strikes the ground.}$ $\text{Apply conservation of mechanical energy (Initial (Kinetic + potential) energy = final (Kinetic + potential) energy)}$ $0 + \left(-\frac{GMm}{R_e + R_e}\right) = \frac{1}{2}mv^2 - \frac{GMm}{R_e}$ $\Rightarrow \frac{1}{2}mv^2 = \frac{GMm}{2R_e} \Rightarrow v = \left(\frac{GM}{R_e}\right)^{\frac{1}{2}}$ $\Rightarrow v = \sqrt{gR_e} \text{ where, } g = \frac{GM}{R_e^2}$

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
}