Import Question JSON

Current Question (ID: 9890)

Question:

$\text{A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is:}$

Options:

1. $10 \text{ m/s}$
2. $10\sqrt{30} \text{ m/s}$
3. $40 \text{ m/s}$
4. $20 \text{ m/s}$

Solution:

\text{Hint: Conserve the energy.} \text{Step: Find the velocity attained by the ball.} \text{Using conservation of energy, the initial potential energy at height 20 m will be converted to kinetic energy and potential energy at the final position.} \text{Initial energy: } E_i = mgh_i = mg(20) \text{Final energy: } E_f = \frac{1}{2}mv^2 + mgh_f = \frac{1}{2}mv^2 + mg(0) \text{By conservation of energy: } E_i = E_f mg(20) = \frac{1}{2}mv^2 + mg(0) \text{Simplifying: } g(20) = \frac{1}{2}v^2 g(20) = \frac{1}{2}v^2 v^2 = 2g(20) = 40g \text{Taking } g = 10 \text{ m/s}^2\text{:} v^2 = 40 \times 10 = 400 v = \sqrt{400} = 20 \text{ m/s}

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
}