Import Question JSON

Current Question (ID: 8861)

Question:

$\text{A car travelling at a speed of 30 km/h is brought to rest at a distance of 8 m by applying brakes. If the same car is moving at a speed of 60 km/h, then it can be brought to rest with the same brakes in:}$

Options:

1. $64 \text{ m}$
2. $32 \text{ m}$
3. $16 \text{ m}$
4. $4 \text{ m}$

Solution:

$\text{Hint: } v^2 = u^2 + 2as$ $\text{Step: Find the distance travelled by the car.}$ $\text{Using 3rd equation of motion:}$ $v^2 = u^2 - 2as$ $0 = u^2 - 2as$ $s = \frac{u^2}{2a} \Rightarrow s \propto u^2$ $\frac{s_1}{s_2} = \frac{u_1^2}{u_2^2}$ $s_2 = 8 \times \frac{60^2}{30^2} = 32 \text{ m}$ $\text{Therefore, the distance travelled by car is 32 m.}$ $\text{Hence, option (2) is the correct answer.}$

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
}