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Q.

Gas at a pressure P₀ is contained in a vessel. If the masses of all the molecules are halved and their speeds are same, the resulting pressure P will be equal to

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a

4P₀

b

2P₀

c

P₀

d

P₀/2

answer is D.

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Detailed Solution

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$\begin{array}{l} P = \frac{1}{3} (\frac{mN}{v}) v^{2} \\ \frac{P_{1}}{P_{2}} = \frac{m_{1} v_{1}^{2}}{m_{2} v_{2}^{2}} = \frac{m_{1} v_{1}^{2}}{(\frac{m}{2}) {(v_{1})}^{2}} \\ \frac{P_{1}}{P_{2}} = \frac{m}{\frac{m}{2}} \\ \frac{P_{1}}{P_{2}} = 2 \Rightarrow P_{2} = \frac{P_{1}}{2} \end{array}$

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