Two cylinders fitted with pistons and placed as shown, connected with string through a small tube of negligible volume, are filled with a gas at pressure $P_{o}$ and temperature $T_{o}$ .The radius of smaller cylinder is half of the other. If the temperature is increased to $2 T_{o}$ . The piston of bigger cylinder moves towards left by 1 m. If P is the atmospheric pressure, find the percentage increase in tension of the string after heating.

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$\frac{25}{(\frac{P_{o} - P}{P_{o}})}$

$\frac{25}{(1 - P_{o} / P)}$

$25 (1 - P_{0} / P)$

$\frac{25}{(1 - P / P_{o})}$

answer is A, C.

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Detailed Solution

In fig. I (for the gas)
$p_{1} = p_{o}; V_{1} = (\frac{5}{4} π R^{2}) u n i t s$
$T_{1} = T_{0}; n = n_{0}$
Ideal gas equation $\frac{p_{1} v_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} \to (2)$
$(F_{2} - F_{1} = P_{2} - P_{0}) π R^{2} \to (1)$
Change in tension $= \frac{F_{2} - F_{1}}{F_{1}} \times 100$
$= \frac{100 P_{0}}{4 (P_{o} - P)} = \frac{25}{(1 - \frac{P}{P_{0}})}$