A) \[\frac{RT}{ng}\left[ \frac{{{l}_{1}}-3{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]
B) \[\frac{nRT}{g}\left[ \frac{1}{{{l}_{2}}}+\frac{1}{{{l}_{1}}} \right]\]
C) \[\frac{RT}{g}\left[ \frac{2{{l}_{1}}+{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]
D) \[\frac{nRT}{g}\left[ \frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]
Correct Answer: D
Solution :
| [d] Let A be area of cross section of the cylinder. |
| As the piston is at rest, so the pressure from both the sides should be equal |
| \[\frac{mg}{A}+\frac{nRT}{{{V}_{1}}}=\frac{nRT}{{{V}_{2}}}\] |
| \[\Rightarrow \]\[\frac{mg}{A}+\frac{nRT}{A{{l}_{1}}}=\frac{nRT}{A{{l}_{2}}}\Rightarrow m=\frac{nRT}{g}\left( \frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right)\] |
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