Import Question JSON

Current Question (ID: 9834)

Question:

$\text{A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicycle due to the road is 200 N is directly opposed to the motion. The work done by the cycle on the road is:}$

Options:

1. $+2000 \text{ J}$
2. $-200 \text{ J}$
3. $\text{zero}$
4. $-20000 \text{ J}$

Solution:

$\text{Hint: Apply the concept of work.}$ $\text{Step 1: Find the work done by the friction.}$ $\text{The work done by the frictional force on the cycle is calculated as:}$ $W_{\text{friction on cycle}} = F \times d \times \cos(180°) = 200 \times 10 \times (-1) = -2000 \text{ J}$ $\text{This is because the frictional force (200 N) is opposite to the direction of motion.}$ $\text{Step 2: Apply Newton's third law.}$ $\text{By Newton's third law, the force exerted by the cycle on the road is equal and opposite to the force exerted by the road on the cycle.}$ $\text{However, since the road is not moving, the displacement of the road is zero.}$ $\text{Step 3: Calculate work done by cycle on road.}$ $W_{\text{cycle on road}} = F \times d_{\text{road}} = F \times 0 = 0$ $\text{Therefore, the work done by the cycle on the road is zero.}$

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
}