Import Question JSON

Current Question (ID: 9757)

Question:

$\text{A block of mass } m \text{ is in contact with the cart } (C) \text{ as shown in the figure. The coefficient of static friction between the block and the cart is } \mu. \text{ The acceleration } a \text{ of the cart that will prevent the block from falling satisfies:}$

Options:

1. $a > \frac{mg}{\mu}$
2. $a > \frac{g}{\mu m}$
3. $a \geq \frac{g}{\mu}$
4. $a < \frac{g}{\mu}$

Solution:

$\text{Hint: The weight of the block is balanced by the friction force.}$ $\text{Step 1: Draw the free-body diagram.}$ $\text{The free-body diagram for the block is as shown with forces: weight } mg \text{ downward, normal force } R \text{ rightward, friction force } F \text{ upward, and pseudo force } ma \text{ leftward.}$ $\text{Step 2: Find the condition of no slipping.}$ $\text{Balancing the horizontal forces, } R = ma$ $\text{Now, in order to make the block static w.r.t. the cart is given by;}$ $\mu R \geq mg$ $\Rightarrow \mu ma \geq mg$ $\Rightarrow a \geq \frac{g}{\mu}$ $\text{Hence, option (3) is the correct answer.}$

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
}