Import Question JSON

Current Question (ID: 9704)

Question:

$\text{A body of mass 5 kg is suspended by the strings making angles } 60^\circ \text{ and } 30^\circ \text{ with the horizontal. Then, choose the correct option from the given ones:}$ $\text{(A) } T_1 = 25 \text{ N}$ $\text{(B) } T_2 = 25 \text{ N}$ $\text{(C) } T_1 = 25\sqrt{3} \text{ N}$ $\text{(D) } T_2 = 25\sqrt{3} \text{ N}$

Options:

1. $\text{(A), (B), and (C) only}$
2. $\text{(A) and (B) only}$
3. $\text{(A) and (D) only}$
4. $\text{(A), (B), (C), (D)}$

Solution:

\text{Hint: As the mass is at rest the resultant of forces acting on it will be zero.} \text{Step 1: Draw the free-body diagram.} \text{The mass is acted upon by three forces: weight (50 N downward), tension } T_1 \text{ at } 30° \text{ with horizontal, and tension } T_2 \text{ at } 60° \text{ with horizontal.} \text{Step 2: Balance the forces in the horizontal direction.} T_1 \cos(30°) = T_2 \cos(60°) T_2 = \sqrt{3} \cdot T_1 \quad \text{...(1)} \text{Step 3: Balance the forces in the vertical direction.} 50 = T_1 \sin(30°) + T_2 \sin(60°) \quad \text{...(2)} \text{From equations (1) and (2):} T_1 = 25 \text{ N} T_2 = 25\sqrt{3} \text{ N} \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
}