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. l1 > l and l2 > l Also \[l=\frac{{{l}_{1}}}{1+\gamma \,{{t}_{1}}}=\frac{{{l}_{2}}}{1+\gamma \,{{t}_{2}}}\] Þ \[{{l}_{1}}+\gamma \,{{l}_{1}}{{t}_{2}}={{l}_{2}}+\gamma \,{{l}_{2}}{{t}_{1}}\] Þ \[\gamma =\frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{2}}{{t}_{1}}-{{l}_{1}}{{t}_{2}}}\]You need to login to perform this action.
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