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Current Question (ID: 11262)

Question:

$\text{A spring pendulum is placed on a rotating table. The initial angular velocity of the table is } \omega_0 \text{ and the time period of the pendulum is } T_0\text{. If the angular velocity of the table becomes } 2\omega_0\text{, then the new time period of the pendulum will be:}$

Options:

1. $2T_0$
2. $T_0\sqrt{2}$
3. $\text{the same}$ (Correct)
4. $\frac{T_0}{\sqrt{2}}$

Solution:

$\text{Hint: } T = 2\pi \sqrt{\frac{m}{k}}$ $\text{Explanation: The time period of the spring pendulum is given by the relation}$ $T = 2\pi \sqrt{\frac{m}{k}}$ $\text{The time period of the spring pendulum does not depend upon the angular velocity of the table. Therefore, the time period of the spring remains the same.}$ $\text{Hence, option (3) is the correct answer.}$

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
}