A student is performing an | Physics | JEE ADVANCED 2014

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JEE-ADVANCED-2014

PAPER 1

Question

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 \mathrm{~s}^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) \mathrm{m}$, the gas in the tube is
(Useful information) : $\sqrt{167 \mathrm{RT}}=640 \mathrm{j}^{1 / 2} \mathrm{~mole}^{-1 / 2} ; \sqrt{140 \mathrm{RT}}=590 \mathrm{j}^{1 / 2} \mathrm{~mole}^{-1 / 2}$. The molar masses M in grams are given in the options. Take the value of $\sqrt{\frac{10}{\mathrm{M}}}$ for each gas as given there.)

Select the correct option:

A

Neon ( $M=20, \sqrt{\frac{10}{20}}=\frac{7}{10}$ )

B

Nitrogen ( $M=28, \sqrt{\frac{10}{28}}=\frac{3}{5}$ )

C

Oxygen ( $\mathrm{M}=32, \sqrt{\frac{10}{32}}=\frac{9}{16}$ )

D

Argon $\left(M=36, \sqrt{\frac{10}{36}}=\frac{17}{32}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$$ \mathrm{f}=\frac{1}{4 \ell} \sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}} \& \frac{\Delta \mathrm{f}}{\mathrm{f}}=\frac{\Delta \ell}{\ell} $$
(A) $\mathrm{M}=20 \times 10^{-3} \mathrm{f}=320 \mathrm{~Hz} \quad \Delta \mathrm{f}= \pm 4.5 \mathrm{~Hz} \quad$ Not possible संभव नहीं है
(B) $\mathrm{M}=20 \times 10^{-3} \mathrm{f}=253 \mathrm{~Hz} \quad \Delta \mathrm{f}= \pm 3.6 \mathrm{~Hz} \quad$ Not possible संभव नहीं है
(C) $\mathrm{M}=32 \times 10^{-3} \mathrm{f}=237 \mathrm{~Hz} \quad \Delta \mathrm{f}= \pm 3.4 \mathrm{~Hz} \quad$ Not possible संभव नहीं है
(D) $M=36 \times 10^{-3} \mathrm{f}=242.8 \mathrm{~Hz} \quad \Delta \mathrm{f}= \pm 3.5 \mathrm{~Hz}$ possible संभव है

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Physics

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