A) \[\frac{2{{a}^{2}}c}{b}\]
B) \[\frac{39}{2{{b}^{2}}c}\]
C) \[\frac{2ac}{{{b}^{2}}}\]
D) \[\frac{3c}{2a{{b}^{2}}}\]
Correct Answer: B
Solution :
As, \[\Delta l=\frac{FL}{AY}\] For steel, \[\Delta {{l}_{A}}=\frac{{{F}_{S}}{{L}_{S}}}{{{A}_{S}}{{Y}_{S}}}\] and for brass \[\Delta {{l}_{B}}=\frac{{{F}_{B}}{{L}_{B}}}{{{A}_{B}}{{Y}_{B}}}\] Then, \[\frac{\Delta {{l}_{S}}}{\Delta {{l}_{B}}}=\frac{{{F}_{S}}}{{{F}_{B}}}\times \frac{{{L}_{S}}}{{{L}_{B}}}\times \frac{{{A}_{B}}}{{{A}_{S}}}\times \frac{{{Y}_{B}}}{{{Y}_{S}}}\] \[=\frac{3m}{2m}\times a\times \frac{1}{{{b}^{2}}}\times \frac{1}{c}\] (according to question) \[\frac{\Delta {{l}_{S}}}{\Delta {{l}_{B}}}=\frac{39}{2{{b}^{2}}c}\]
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