Import Question JSON

Current Question (ID: 9779)

Question:

$\text{Two masses, A and B, each of mass } M \text{ are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass B starts moving away from mass A with acceleration } a \text{ in the ground frame, then the acceleration of mass A will be:}$

Options:

1. $\frac{Ma - F}{M}$
2. $\frac{MF}{F + Ma}$
3. $\frac{F + Ma}{M}$
4. $\frac{F - Ma}{M}$

Solution:

$\text{Hint: Net force on mass B = F - Ma}$ $\text{Step 1: Identify the state of spring}$ $\text{The spring connects masses A and B, and when force F is applied to B, the spring gets compressed or extended}$ $\text{Step 2: Write force equation for mass B}$ $F - F_{sp} = Ma$ $\text{where } F_{sp} \text{ is the spring force acting on mass B}$ $\text{Step 3: Write force equation for mass A}$ $F_{sp} = Ma_A$ $\text{where } a_A \text{ is the acceleration of mass A}$ $\text{From the force equation for mass B: } F_{sp} = F - Ma$ $\text{Substituting into the equation for mass A:}$ $F - Ma = Ma_A$ $\text{Therefore: } a_A = \frac{F - Ma}{M}$

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
}