A) \[\frac{\sqrt{hc}}{{{c}^{\frac{3}{2}}}}\]
B) \[\frac{\sqrt{hc}}{{{c}^{\frac{5}{2}}}}\]
C) \[\sqrt{\frac{hc}{G}}\]
D) \[\sqrt{\frac{Gc}{{{h}^{\frac{3}{2}}}}}\]
Correct Answer: A
Solution :
\[L\,\alpha \,{{h}^{a}}{{c}^{b}}{{G}^{c}}\] \[{{[L]}^{1}}={{[{{M}^{1}}{{L}^{2}}{{T}^{-1}}]}^{a}}{{[L{{T}^{-1}}]}^{b}}{{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]}^{c}}\] Solving, \[a=\frac{1}{2},c=\frac{1}{2},b=\frac{3}{2}\] \[\Rightarrow L=\frac{\sqrt{hG}}{{{c}^{\frac{3}{2}}}}\]
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