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  • A quantity f is given by  where c is speed on light, G is universal gravitational constant

A quantity f is given by f = \sqrt{\frac{hc^5}{G}} where c is speed on light, G is universal gravitational constant and h is the Plank's constant. Dimension of f is that of:
Option: 1 area
Option: 2 volume
Option: 3 Momentum
Option: 4 energy

Answers (1)

best_answer

 

             \sqrt{\frac{h c^{5}}{G}}=\sqrt{\frac{\left[M L^{2} T^{-1}\right]\left[L T^{-1}\right]^{5}}{\left[M^{-1} L^{3} T^{-2}\right]}}  

            \\ \sqrt{\frac{hc^5}{G}} = \sqrt{\frac{[ML^7T^{-6}]}{[M^{-1}L^3T^{-2}]}} \\ \\ \\ \Rightarrow \sqrt{[M^2L^4T^{-4}]} = ML^2T^{-2} 

   ML^2T^{-2} is also the dimension of energy. 

 

                 Hence the option correct option is (4).  

Posted by

avinash.dongre

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