Import Question JSON

Current Question (ID: 19148)

Question:

$\text{A curve in a level road has a radius of } 75 \text{ m. The maximum speed of a car turning this curved road can be } 30 \text{ m/s without skidding. If the radius of the curved road is changed to } 48 \text{ m and the coefficient of friction between the tyres and the road remains the same, then the maximum allowed speed would be:}$

Options:

1. $12 \text{ m/s}$
2. $24 \text{ m/s}$
3. $32 \text{ m/s}$
4. $44 \text{ m/s}$

Solution:

$\text{Hint: } v = \sqrt{\mu r g}$ $\text{Step: Find the new maximum allowed speed.}$ $\text{The maximum allowed speed of the particle is given by:}$ $v = \sqrt{\mu r g}$ $\Rightarrow v \propto \sqrt{r}$ $\text{The ratio of allowed speed is given by:}$ $\Rightarrow \frac{v_1}{v_2} = \sqrt{\frac{r_1}{r_2}}$ $\Rightarrow v_2 = v_1 \times \sqrt{\frac{r_2}{r_1}} = 30 \times \sqrt{\frac{48}{75}}$ $\Rightarrow v_2 = 30 \times \sqrt{\frac{16}{25}} = 30 \times \frac{4}{5} = 24 \text{ m/s}$ $\text{Hence, option (2) is the correct answer.}$

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
}