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Current Question (ID: 9777)

Question:

$\text{As shown in the figure, two masses of } 10 \text{ kg and } 20 \text{ kg, respectively are connected by a massless spring. A force of } 200 \text{ N acts on the } 20 \text{ kg mass. At the instant shown, the } 10 \text{ kg mass has an acceleration of } 12 \text{ m/s}^2 \text{ towards the right. The acceleration of } 20 \text{ kg mass at this instant is:}$

Options:

1. $12 \text{ m/s}^2$
2. $4 \text{ m/s}^2$
3. $10 \text{ m/s}^2$
4. $\text{zero}$

Solution:

$\text{Hint: The spring force will be the same on both blocks.}$ $\text{Step 1: Find the magnitude of the spring force.}$ $\text{For the 10 kg block, applying Newton's second law:}$ $f_s = ma = 10 \times 12 = 120 \text{ N}$ $\text{Step 2: Find the acceleration of 20 kg block.}$ $\text{For the 20 kg block, the net force equation is:}$ $F - f_s = ma$ $200 - 120 = 20a$ $\Rightarrow a = 4 \text{ m/s}^2$ $\text{Hence, option (2) is the correct answer.}$

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
}