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Current Question (ID: 10317)

Question:

$\text{A uniform rod of length } 1 \text{ m and mass } 2 \text{ kg is suspended by two vertical inextensible strings as shown in the following figure. The tension } T \text{ (in newtons) in the left string at the instant when the right string snaps is:}$ $(g = 10 \text{ m/s}^2)$

Options:

1. $2.5 \text{ N}$
2. $5 \text{ N}$
3. $7.5 \text{ N}$
4. $10 \text{ N}$

Solution:

$\text{When the right string snaps, the rod begins to rotate about the left string.}$ $\text{At the instant when the right string snaps, we apply Newton's second law for rotation.}$ $\text{The equation of motion is: } Mg - T = Ma_y$ $\text{For rotational motion about the left end:}$ $T\left(\frac{l}{2}\right) = \frac{Ml^2}{12}\alpha$ $\text{where } a_y = \frac{l}{2}\alpha$ $\text{Substituting the values and solving:}$ $T = \frac{Mg}{4} = \frac{2 \times 10}{4} = 5 \text{ N}$

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
}