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Mechanics

If velocity of light c, Planck's constant h and gravitational constant G are taken as fundamental quantities, then express mass and length in terms of dimensions of these quantities.

Profile image of Aditya
8 Years agoGrade
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1 Answer

Profile image of Khimraj
8 Years ago

Here, [c]=LT1 
[G]=M1L3T2
[h]=M1L2T1
Let m α cxGyhz

By substituting the dimensions of each quantity in both the sides,

L=(LT1)x(M1L3T2)y(ML2T1)z
L=[My+zLx+3y+2zTx2yz]

on solving x = -3/2, y = ½, z = ½ 

so L = [c-3/2h1/2G1/2]

Hope it clears.