Import Question JSON

Current Question (ID: 9805)

Question:

$\text{One end of the string of length } l \text{ is connected to a particle of mass } m \text{ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed } v\text{, the net force on the particle (directed towards the centre) will be: (}T \text{ represents the tension in the string)}$

Options:

1. $T$
2. $T + \frac{mv^2}{l}$
3. $T - \frac{mv^2}{l}$
4. $\text{zero}$

Solution:

$\text{Consider the string of length l connected to a particle as shown in the figure.}$ $\text{Speed of the particle is V. As the particle is in uniform circular motion, net force on the particle must be equal to centripetal force which is provided by the tension (T)}$ $\therefore \text{Net force} = \text{Centripetal force}$ $\Rightarrow \frac{mv^2}{l} = T$

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
}