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Current Question (ID: 11271)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): If the bob of a simple pendulum is kept in a horizontal electric field, its period of oscillation will remain the same.}$ $\text{Reason (R): If bob is charged and kept in a horizontal electric field, then the time period will be decreased.}$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{(A) is False but (R) is True.}$ (Correct)

Solution:

$\text{The correct option is 4.}$ $\text{Here's the breakdown:}$ $\text{Assertion (A): The assertion states that the period of oscillation of a simple pendulum stays the same when it's in a horizontal electric field. This is false.}$ $\text{When the charged bob is in a horizontal electric field, it experiences an additional electric force. This force, along with gravity, creates a new, larger effective gravitational acceleration.}$ $\text{Because the period of a pendulum is inversely related to the square root of the gravitational acceleration } (T \propto 1/\sqrt{g})\text{, an increase in the effective acceleration will decrease the period.}$ $\text{Reason (R): The reason states that the period will decrease. This is true.}$ $\text{As explained above, the combination of gravitational and electric forces increases the net acceleration on the bob.}$ $\text{A higher net acceleration makes the pendulum swing back and forth more quickly, thus reducing its period.}$ $\text{In conclusion, Assertion (A) is false, but Reason (R) is true.}$

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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
}