Import Question JSON

Current Question (ID: 11282)

Question:

$\text{A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:}$

Options:

1. $\text{the speed of block starts decreasing but acceleration starts increasing.}$ (Correct)
2. $\text{the speed of the block as well as its acceleration starts decreasing.}$
3. $\text{the speed of the block starts increasing but its acceleration starts decreasing.}$
4. $\text{the speed of the block as well as acceleration start increasing.}$

Solution:

$\text{Initially, the spring is at its natural length, and the block is given a velocity towards the right. The block starts to move and compress the spring.}$ \\ $\text{According to Hooke's law, the restoring force exerted by the spring is given by } F = -kx\text{, where } x \text{ is the displacement from the equilibrium position (the relaxed spring position).}$ \\ $\text{As the block moves to the right, the displacement } x \text{ increases.}$ \\ $\text{The force } F \text{ from the spring acts in the direction opposite to the displacement, so it acts to the left, opposing the block's motion. This causes the speed of the block to decrease.}$ \\ $\text{As the block continues to compress the spring, the displacement } x \text{ increases, so the magnitude of the restoring force } F \text{ also increases. Since } F=ma\text{, an increasing force means an increasing acceleration.}$ \\ $\text{Thus, the speed of the block decreases, while the magnitude of its acceleration increases.}$

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
}