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