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Current Question (ID: 9772)

Question:

$\text{The block of mass } m \text{ (shown in the figure) does not move on applying the inclined force } F. \text{ The friction force acting on the block is:}$

Options:

1. $F \cos \theta$
2. $F \sin \theta$
3. $\mu mg - F \sin \theta$
4. $\mu mg$

Solution:

$\text{Hint: Block will not move if } F_H = f_s$ $\text{Step 1: Resolve the force, F.}$ $\text{The applied force } F \text{ at angle } \theta \text{ can be resolved into:}$ $\text{- Horizontal component: } F \cos \theta \text{ (along the surface)}$ $\text{- Vertical component: } F \sin \theta \text{ (perpendicular to the surface)}$ $\text{Step 2: Find friction force acting on the block.}$ $\text{Since the block does not move, it is in equilibrium. For horizontal equilibrium:}$ $\text{The friction force must balance the horizontal component of the applied force.}$ $\text{Therefore: } f = F \cos \theta$ $\text{The friction force acts opposite to the horizontal component of the applied force to maintain equilibrium.}$ $\text{The vertical component } F \sin \theta \text{ affects the normal force but not the friction force directly.}$

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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
}