Import Question JSON

Current Question (ID: 19156)

Question:

$\text{In two different experiments, an object of mass } 5 \text{ kg moving with a speed of } 25 \text{ ms}^{-1} \text{ hits two different walls and comes to rest within } (i) \ 3 \text{ s, and } (ii) \ 5 \text{ s, respectively.}$ $\text{Choose the correct option from the following:}$

Options:

1. $\text{Impulse and average force acting on the object will be the same for both the cases.}$
2. $\text{Impulse will be the same for both the cases but the average force will be different.}$
3. $\text{The average force will be the same for both the cases but the impulse will be different.}$
4. $\text{Average force and impulse will be different for both the cases.}$

Solution:

$\text{Hint: Impulse = change in momentum.}$ $\text{Step: Analyse each option one by one.}$ $\text{The impulse is the change in momentum, which is given by:}$ $\text{Impulse} = \Delta p = p_f - p_i$ $\text{Given: } m = 5 \text{ kg}, u = 25 \text{ m/s}, v = 0 \text{ m/s}$ $\text{Impulse} = \Delta p = p_f - p_i = 5 \times (0 - 25) = -125 \text{ kg-m/s}$ $\text{Since the impulse depends only on the initial and final velocities and the mass, the impulse will be the same in both cases.}$ $\text{Impulse in terms of average force is given by:}$ $\text{Impulse} = F_{\text{avg}} \cdot \Delta t, \text{ where } \Delta t \text{ is the time over which the force acts.}$ $\text{Since the impulse is the same, but the time duration is different, the average force } F_{\text{avg}} \text{ will be different for each case.}$ $\text{Specifically, the average force will be larger in the case where the object stops in } 3 \text{ seconds (because the same impulse is delivered over a shorter time).}$ $\text{Hence, option (2) is the correct answer.}$

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
}