Import Question JSON

Current Question (ID: 9822)

Question:

$\text{A body constrained to move along the z-axis of a coordinate system is subjected to constant force given by } \vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k} \text{ where } \hat{i}, \hat{j} \text{ and } \hat{k} \text{ are unit vectors along the x-axis, y-axis and z-axis of the system respectively. The work done by this force in moving the body a distance of 4 m along the z-axis will be:}$

Options:

1. $15 \text{ J}$
2. $14 \text{ J}$
3. $13 \text{ J}$
4. $12 \text{ J}$

Solution:

$\text{Hint: The work done is given by the dot product of the force and the displacement.}$ $\text{Step: The force acting on the body is}$ $\vec{F} = -\hat{i} + 2\hat{j} + 3\hat{k}$ $\text{The work done to move the object on the z-axis is due to the z-component of force.}$ $W = \vec{F} \cdot \vec{s}$ $= (-\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (4\hat{k})$ $= 12 \text{ J}$ $\text{Hence, option (4) is the correct answer.}$

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
}