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Current Question (ID: 19998)

Question:

$\text{The mass per unit length of a uniform wire is } 0.135 \text{ g/cm. A transverse wave of the form } y = -0.21 \sin(x + 30t) \text{ is produced in it, where } x \text{ is in meter and } t \text{ is in second. The expected value of the tension in the wire is:}$

Options:

1. $12.15 \text{ N}$
2. $30.12 \text{ N}$
3. $45.35 \text{ N}$
4. $50.24 \text{ N}$

Solution:

$v = \sqrt{\frac{T}{\mu}}$ $\text{Find the value of tension in the wire.}$ $\text{Given: } \mu = 0.135 \text{ gm/cm } = 0.0135 \text{ kg/m}$ $y = -0.21 \sin(x + 30t)$ $\text{where } x \text{ is in meters and } t \text{ is in seconds}$ $\text{The wave velocity of the transverse wave is given by:}$ $v = \frac{\omega}{k} = \frac{30}{1} \text{ m/s} = \sqrt{\frac{T}{\mu}}$ $\Rightarrow T = \mu \times 30^2$ $\Rightarrow T = 0.0135 \times 900 = 12.15 \text{ N}$ $\text{Hence, option (1) is the correct answer.}$

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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
}