Import Question JSON

Current Question (ID: 19234)

Question:

$\text{A wedge of mass } M = 4m \text{ lies on a frictionless surface. A particle of mass } m \text{ approaches the wedge with speed } v. \text{ There is no friction between the particle and the plane, nor between the particle and the wedge. The maximum height reached by the particle on the wedge is given by:}$

Options:

1. $\frac{2v^2}{7g}$
2. $\frac{v^2}{2g}$
3. $\frac{2v^2}{5g}$
4. $\frac{v^2}{g}$

Solution:

$\text{Hint: Apply conservation of momentum and energy.}$ $\text{Step: Find the maximum height climbed by the particle on the wedge.}$ $\text{The motion of the particle is on the wedge is shown by:}$ $\text{By applying conservation of momentum we get:}$ $mv = 5mv' \Rightarrow v' = \frac{v}{5}$ $\text{By applying the conservation of energy we get:}$ $\frac{1}{2}mv^2 = \frac{1}{2} \times 5mv'^2 + mgh$ $\Rightarrow \frac{v^2}{2} = \frac{5}{2} \times \left(\frac{v}{5}\right)^2 + gh$ $\Rightarrow \frac{v^2}{2} - \frac{v^2}{10} = gh$ $\Rightarrow \left(\frac{2}{5}\right)v^2 = gh$ $\Rightarrow h = \frac{2v^2}{5g}$ $\text{Hence, option (3) is the correct answer.}$

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
}