Import Question JSON

Current Question (ID: 9595)

Question:

$\text{A body started moving with an initial velocity of 4 m/s along the east and an acceleration 1 m/s}^2 \text{ along the north. The velocity of the body just after 4 s will be?}$

Options:

1. $8 \text{ m/s along East.}$
2. $4\sqrt{2} \text{ m/s along North-East.}$
3. $8 \text{ m/s along North.}$
4. $4\sqrt{2} \text{ m/s along South-East.}$

Solution:

\text{Hint: } \vec{v} = \vec{u} + \vec{a}t \text{Step: Find the velocity of the body just after 4 s.} \text{Given: } \vec{u} = 4\hat{i} \text{ m/s, } \vec{a} = 1\hat{j} \text{ m/s}^2 \text{By using 1st equation of motion } \vec{v} = \vec{u} + \vec{a}t \vec{v} = 4\hat{i} + (1\hat{j}) \cdot 4 \vec{v} = 4\hat{i} + 4\hat{j} \text{The magnitude of velocity:} |\vec{v}| = \sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \text{ m/s} \text{The direction is along North-East since both} \text{ components are equal and positive.} \text{Therefore, the velocity of the body just after 4 s is } 4\sqrt{2} \text{ m/s along North-East.} \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
}