A) \[\frac{{{b}^{2}}a}{2c}\]
B) \[\frac{bc}{2{{a}^{2}}}\]
C) \[\frac{b{{a}^{2}}}{2c}\]
D) \[\frac{a}{2{{b}^{2}}c}\]
Correct Answer: D
Solution :
Let Youngs modulus of steel and brass are \[{{Y}_{1}}\] and \[{{Y}_{2}}\] respectively. \[\therefore \] \[{{Y}_{1}}=\frac{{{F}_{1}}}{{{A}_{1}}}\cdot \frac{{{l}_{1}}}{\Delta {{l}_{1}}}\]and \[{{Y}_{2}}=\frac{{{F}_{2}}}{{{A}_{2}}}\cdot \frac{{{l}_{2}}}{\Delta {{l}_{2}}}\] Now, free body diagram of the two blocks are Force on steel wire \[T={{F}_{1}}=2g\,N.\] Force on brass wire\[{{F}_{2}}=T=T+2g=4g\,N\] \[\frac{{{Y}_{1}}}{{{Y}_{2}}}=\,\,\,\left( \frac{2g}{4g} \right)\cdot \left( \frac{\pi r_{2}^{2}}{\pi r_{1}^{2}} \right)\left( \frac{{{l}_{1}}}{{{l}_{2}}} \right)\cdot \left( \frac{\Delta {{l}_{2}}}{\Delta {{l}_{1}}} \right)\] \[c=\frac{1}{2}\cdot \frac{1}{{{b}^{2}}}\cdot a\cdot \frac{\Delta {{l}_{2}}}{\Delta {{l}_{1}}}\] or \[\frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{a}{2{{b}^{2}}c}\]You need to login to perform this action.
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