A) \[{{V}^{-2}}{{A}^{2}}{{F}^{-2}}\]
B) \[{{V}^{-2}}{{A}^{2}}{{F}^{2}}\]
C) \[{{V}^{-4}}{{A}^{2}}F\]
D) \[{{V}^{-4}}{{A}^{-2}}F\]
Correct Answer: C
Solution :
Young's modulus,\[Y=\frac{F/A}{\Delta l/l}\] Dimensionally,\[Y=\frac{F}{{{(length)}^{2}}}=\frac{F}{{{(speed)}^{2}}{{(time)}^{2}}}\] \[=\frac{F}{{{(speed)}^{2}}{{\left( \frac{Speed}{Acceleration} \right)}^{2}}}\] \[[Y]=[F\,{{V}^{-4}}{{A}^{2}}]\]
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