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Current Question (ID: 19158)

Question:

$\text{In the figure shown, two blocks of masses } m_1 = 4 \text{ kg and } m_2 = 1 \text{ kg are placed over a smooth fixed wedge, connected by an ideal string over a smooth pulley. As the system is released, the tension in the string will be:}$

Options:

1. $4(\sqrt{3} + 1) \text{ N}$
2. $10\left(1 - \frac{1}{\sqrt{3}}\right) \text{ N}$
3. $10(\sqrt{3} - 1) \text{ N}$
4. $\frac{10}{3}(\sqrt{3} - 1) \text{ N}$

Solution:

$\text{Hint: Use Newton's second law } \vec{F} = m\vec{a}$ $\text{Step 1: Find the acceleration of the system.}$ $\text{The acceleration of the system is given by:}$ $a = \frac{F_{\text{net}}}{M}$ $\Rightarrow a = \frac{4 \times g \sin(60^\circ) - g \sin(30^\circ)}{4+1}$ $\Rightarrow a = (4\sqrt{3} - 1) \text{ m/s}^2$ $\text{Step 2: Find the tension in the string.}$ $\text{Applying the equation of motion along the wedge for 4 kg block:}$ $40 \sin 60^\circ - T = 4a$ $\Rightarrow T = 40 \sin 60^\circ - 4a \quad [a = (4\sqrt{3} - 1)]$ $\Rightarrow 4(\sqrt{3} + 1) \text{ N}$ $\text{Hence, option (1) is the correct answer.}$

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
}