A) \[\frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{2}}{{t}_{1}}-{{l}_{1}}{{t}_{2}}}\]
B) \[\frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{1}}{{t}_{1}}-{{l}_{2}}{{t}_{2}}}\]
C) \[\frac{{{l}_{1}}+{{l}_{2}}}{{{l}_{2}}{{t}_{1}}+{{l}_{1}}{{t}_{2}}}\]
D) \[\frac{{{l}_{1}}+{{l}_{2}}}{{{l}_{1}}{{t}_{1}}+{{l}_{2}}{{t}_{2}}}\]
Correct Answer: A
Solution :
Suppose, height of liquid in each arm before rising the temperature is \[l\]. |
With temperature rise height of liquid in each arm increases i.e. \[{{l}_{1}}>l\] and \[{{l}_{2}}>l\] |
Also \[l=\frac{{{l}_{1}}}{1+\gamma \,{{t}_{1}}}=\frac{{{l}_{2}}}{1+\gamma {{t}_{2}}}\] |
\[\Rightarrow \,\,{{l}_{1}}+\gamma {{l}_{1}}{{t}_{2}}={{l}_{2}}+\gamma {{l}_{2}}{{t}_{1}}\Rightarrow \gamma =\frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{2}}{{t}_{1}}-{{l}_{1}}{{t}_{2}}}\] |
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