Import Question JSON

Current Question (ID: 9799)

Question:

$\text{A body of mass } m \text{ is moving on a concave bridge } ABC \text{ of the radius of curvature } R \text{ at a speed } v. \text{ The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:}$

Options:

1. $mg - \frac{mv^2}{R}$
2. $mg + \frac{mv^2}{R}$
3. $mg$
4. $\frac{mv^2}{R}$

Solution:

$\text{Hint: Use the concept of centripetal force.}$ $\text{Step: Find normal reaction of the bridge on the body.}$ $\text{The normal reaction of the bridge on the body is given by:}$ $F_c = N - mg$ $N - mg = \frac{mv^2}{R}$ $\Rightarrow N = mg + \frac{mv^2}{R}$ $\text{Hence, option (2) is the correct answer.}$

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
}