JEE Main · PhysicsHard

$If the velocity of light $c$, gravitational constant $G$, and Planck constant $h$ are chosen as fundamental units, the dimension of mass in this system is proportional to which of the following?$

Show correct answer & step-by-step solution

Correct answer: A — $\sqrt{\frac{hc}{G}}$

Solution

Using dimensional analysis,

[M] = [c]^{x} [G]^{y} [h]^{z}

. Substituting dimensions:

[M] = [L T^{- 1}]^{x} [M^{- 1} L^{3} T^{- 2}]^{y} [M L^{2} T^{- 1}]^{z}

. Solving the system of equations for

x, y, z

gives

M \propto \frac{h c}{G}