Import Question JSON

Current Question (ID: 19163)

Question:

$\text{A car is moving on a circular track of radius } 50 \text{ cm with coefficient of friction being } 0.34. \text{ On this horizontal track, the maximum safe speed for turning is equal to:}$ $\text{(take } g = 10 \text{ m/s}^2 )$

Options:

1. $1.03 \text{ m/s}$
2. $1.7 \text{ m/s}$
3. $1.3 \text{ m/s}$
4. $1.8 \text{ m/s}$

Solution:

$\text{Hint: Friction will provide the required centripetal acceleration to move in the circle.}$ $\text{Step: Find the maximum safe speed for turning a car.}$ $\text{As friction will provide the required centripetal acceleration to move in the circle i.e.,}$ $\frac{mv^2}{r} = \mu mg$ $\Rightarrow v = \sqrt{\mu g R}$ $\Rightarrow v = \sqrt{0.34 \times 10 \times \frac{1}{2}} \quad \left[ R = \frac{50}{100} = \frac{1}{2} \text{ m} \right]$ $\Rightarrow v = \sqrt{1.7} = 1.3 \text{ m/s}.$ $\text{Therefore, the maximum safe speed for turning a car is } 1.3 \text{ m/s.}$ $\text{Hence, option (3) is the correct answer.}$

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
}