Import Question JSON

Current Question (ID: 19261)

Question:

$\text{The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block.}$ $\text{Assume that bullet is facing constant resistance during its motion in the block.}$ $\text{The bullet stops completely after travelling at } (4 + x) \text{ cm inside the block.}$ $\text{The value of } x \text{ is:}$

Options:

1. $2.0$
2. $1.0$
3. $0.5$
4. $1.5$

Solution:

$\text{Hint: Apply the work energy theorem.}$ $\text{Step: Find the value of } x.$ $W_{\text{Resistive force}} = \Delta K.E$ $\Rightarrow -F \times 4 = \frac{1}{2} m \left( \frac{v^2}{9} - v^2 \right) \quad \ldots (1)$ $\Rightarrow -F \times (4 + x) = \frac{1}{2} m (0 - v^2) \quad \ldots (2)$ $\text{By dividing eqn (1) by (2) we get;}$ $\frac{4}{4+x} = \frac{8}{9}$ $\Rightarrow 36 = 32 + 8x$ $\Rightarrow x = \frac{1}{2} = 0.5$ $\text{Hence, option (3) is the correct answer.}$

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
}