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Current Question (ID: 19358)

Question:

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

Options:

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

Solution:

$\text{Hint: } \vec{F}_{\text{net}} = M\vec{a}$ $\text{Step: Find the acceleration of the mass } B.$ $\text{Let the spring is initially compressed then when the spring is}$ $\text{released, it will push mass } A \text{ toward the right and mass } B \text{ towards}$ $\text{the left i.e., mass } A \text{ moves away from mass } B.$ $\text{Using } \vec{F}_{\text{net}} = M\vec{a},$ $-\hat{i}F = m_A a_A \hat{i} + m_B \vec{a}_B$ $\Rightarrow -\hat{i}F - M a_A \hat{i} = M \vec{a}_B \quad [m_A = m_B = M]$ $\Rightarrow \vec{a}_B = \frac{-\hat{i}(F + Ma)}{M}$ $\text{The negative sign indicates that the direction of mass } B \text{ is towards}$ $\text{the left and the magnitude of the acceleration of the mass } B \text{ is}$ $\frac{F + Ma}{M}.$ $\text{Hence, option } (3) \text{ is the correct answer.}$

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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
}