Import Question JSON

Current Question (ID: 9627)

Question:

$\text{Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are } v_1, v_2 \text{ and } v_3 \text{ respectively, then:}$

Options:

1. $v_1 > v_2 > v_3$
2. $v_3 > v_2 = v_1$
3. $v_1 = v_2 = v_3$
4. $v_1 < v_2 < v_3$

Solution:

$\text{Hint: When particles are thrown at any angle but with the same speed, they will have the same speed at the same height.}$ $\text{Step 1: For particle 1:}$ $v_{1,x}^2 + v_{1,y}^2 = v^2$ $v_{1,y}^2 = v_{1,y}^2 + 2gh$ $\text{The final velocity of the particle 1:}$ $v_1^2 = v_{1,x}^2 + v_{1,y}^2 = v_{1,x}^2 + v_{1,y}^2 + 2gh = v^2 + 2gh$ $\text{Step 2: For particle 2:}$ $v_y^2 = 0 + 2gh$ $v_2^2 = v^2 + v_y^2 = v^2 + 2gh$ $\text{Step 3: For particle 3:}$ $v^2 = v_{3,x}^2 + v_{3,y}^2$ $\text{Similarly, for particle 3, the final speed is also } v^2 + 2gh$ $\text{Therefore, all three particles have the same final speed when they hit the ground: } v_1 = v_2 = v_3$

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
}