A) \[\Delta l\] versus \[\frac{1}{l}\]
B) \[\Delta l\] versus \[{{l}^{2}}\]
C) \[\Delta l\] versus \[\frac{1}{{{l}^{2}}}\]
D) \[\Delta l\] versus \[l\]
Correct Answer: B
Solution :
| For Hooke's law. Young Modulus |
| \[y=\frac{F/A}{\Delta l/l}=\frac{F\times l}{\Delta l\times A}\] |
| \[V=A\times l=\] constant |
| From Eqs. (i) and (ii), |
| \[y=\frac{F\times l\times l}{\Delta l\times V}\] (i) |
| \[\Delta \,l=\frac{F}{V\times y}{{l}^{2}}\] (ii) |
| \[\Rightarrow \] \[\Delta l\propto {{l}^{2}}\] |
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