Import Question JSON

Current Question (ID: 10242)

Question:

$\text{A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the path followed by its center of mass?}$

Options:

1. $\text{Ladder moves in a straight line downward and to the right}$
2. $\text{Ladder moves in a curved path downward and to the right}$
3. $\text{Ladder moves in a straight line downward and to the left}$
4. $\text{Ladder moves in a curved path downward and to the left}$

Solution:

$\text{Hint: Recall the motion of centre of mass.}$ $\text{Explanation: The forces acting on the ladder are shown in the figure.}$ $\text{The ladder experiences:}$ $\text{1. Weight } mg \text{ acting downward at the center of mass}$ $\text{2. Normal reaction } R_1 \text{ from the wall acting horizontally}$ $\text{3. Normal reaction } R_2 \text{ from the floor acting vertically upward}$ $\text{Due to net force in the downward direction, the centre of mass will go down. Therefore, option (1) represents the path followed by its center of mass.}$ $\text{Hence, option (1) is the correct answer.}$

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
}