question_answer

A quantity f is given by \[f=\sqrt{\frac{h{{c}^{5}}}{G}}\] where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of                            [JEE MAIN Held on 09-01-2020 Morning]

A) Energy

B) Area

C) Volume

D) Momentum

Correct Answer: A

Solution :

[a] \[\frac{hc}{\lambda }=E\Rightarrow \left[ hc \right]=\left[ M{{L}^{2}}{{T}^{-2}} \right]\left[ L \right]=\left[ M{{L}^{3}}{{T}^{-2}} \right]\] \[[c]=[L{{T}^{-1}}]\] \[[G]=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]    \[\Rightarrow \,\,\,\,\left[ \sqrt{\frac{h{{c}^{5}}}{G}} \right]=\left[ M{{L}^{2}}{{T}^{-2}} \right]=\]Energy