Import Question JSON

Current Question (ID: 11259)

Question:

$\text{If the length of a pendulum is made 9 times and the mass of the bob is made 4 times, then the value of time period will become:}$

Options:

1. $3T$ (Correct)
2. $\frac{3}{2}T$
3. $4T$
4. $2T$

Solution:

$\text{Hint: } T = 2\pi\sqrt{\frac{l}{g}}$ $\text{Step: Find the relation between the time periods of the pendulum.}$ $\text{The initial time period is given by:}$ $T = 2\pi\sqrt{\frac{l}{g}} \Rightarrow T \propto \sqrt{l} \ldots (1)$ $\text{If } l \text{ is made 9 times, the new length will be } 9l.$ $\text{The final time period is given by:}$ $\Rightarrow T_f \propto \sqrt{9l} \Rightarrow T_f \propto 3\sqrt{l} \ldots (2)$ $\text{Dividing (1) and (2), we get:}$ $\Rightarrow \frac{T_f}{T} = \frac{3\sqrt{l}}{\sqrt{l}} \Rightarrow T_f = 3T$ $\text{The time period of the simple pendulum does not depend on the mass of the bob.}$ $\text{Hence, option (1) is the correct answer.}$

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
}