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Current Question (ID: 10350)

Question:

$\text{The length of an elastic string is } a \text{ metre when the longitudinal tension is 4 N and } b \text{ metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N will be:}$

Options:

1. $a - b$
2. $5b - 4a$
3. $2b - \frac{1}{4}a$
4. $4a - 3b$

Solution:

\text{Let } L \text{ be the original length of the wire and } K \text{ be the force constant of the wire.} \text{Final length = initial length + elongation} L' = L + \frac{F}{K} \text{For first condition: } a = L + \frac{4}{K} \quad \text{...(i)} \text{For second condition: } b = L + \frac{5}{K} \quad \text{...(ii)} \text{By solving equations (i) and (ii), we get:} L = 5a - 4b \quad \text{and} \quad K = \frac{1}{b-a} \text{Now when the longitudinal tension is 9N, length of the string:} \text{Length} = L + \frac{9}{K} = 5a - 4b + 9(b - a) = 5b - 4a

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
}