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Current Question (ID: 19105)

Question:

$\text{Two projectiles, } A \text{ and } B \text{ are projected from the same point } (O) \text{ on the ground with the same initial speed, as shown in the figure.}$ $\text{The ratio of maximum height attained by the projectile } A \text{ to that attained by projectile } B \text{ is:}$

Options:

1. $3 : 1$
2. $1 : 3$
3. $\sqrt{3} : 1$
4. $\sqrt{3} : 2$

Solution:

$\text{Hint: } H = \frac{u^2 \sin^2 \theta}{2g}$ $\text{Step: Find the ratio of maximum height attained by the given projectiles.}$ $\text{The maximum height of the projectile is given by:}$ $H = \frac{u^2 \sin^2 \theta}{2g}$ $\text{The ratio of maximum height attained by the given projectile is given by:}$ $\frac{H_A}{H_B} = \frac{\frac{u^2 \sin^2 60^\circ}{2g}}{\frac{u^2 \sin^2 30^\circ}{2g}}$ $\Rightarrow \frac{H_A}{H_B} = \frac{\left(\frac{\sqrt{3}}{2}\right)^2}{\left(\frac{1}{2}\right)^2}$ $\Rightarrow \frac{H_A}{H_B} = \frac{3}{1}$ $\text{Therefore, the ratio of maximum height attained by the given projectiles is } 3 : 1.$ $\text{Hence, option (1) is the correct answer.}$

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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
}