If the velocity of light c, the universal gravitational constant G, and the Planck's constant h are chosen as fundamental units, the dimensions of mass in this system are :
Answer & explanation
Correct answer: option 1
[M] = [ha cb Gc]
[ML2T-1]a [LT-1]b [M-1L3T-2]c = [M]
⇒ [Ma-cL2a+b+3cT-a-b-2c] = [M]
a-c =1
2a+b+3c =0
-a-b-2c = 0
On solving for a, b and c,
a = 1/2 ; b = 1/2 ; c = -1/2
[h1/2 c1/2 G-1/2] = [ML2T-1]1/2 [LT-1]1/2 [M-1L3T-2]-1/2
[h1/2 c1/2 G-1/2] = [M]