A quantity f is given by f = √(hc5/G) where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :

Question

A quantity f is given by f = √(hc5/G) where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of : (A) area (B) volume (C) momentum (D) energy

Tardigrade Admin · Accepted Answer

[h]=M1L2T-1 [C]=L1T-1 [G]=M-1L3T-2 [f]=√(M1L2T-1× L5T-5/M-1L3T-2)=M1L2T-2

Q. A quantity f is given by $f = \frac{h c ^{5}}{G}$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :

area

volume

momentum

energy

$[h] = M^{1} L^{2} T^{- 1}$
$[C] = L^{1} T^{- 1}$
$[G] = M^{- 1} L^{3} T^{- 2}$
$[f] = \frac{M ^{1} L ^{2} T ^{- 1} \times L ^{5} T ^{- 5}}{M ^{- 1} L ^{3} T ^{- 2}} = M^{1} L^{2} T^{- 2}$

Q. A quantity f is given by f=Ghc5​​ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :