Question

if the velocity of light C gravitational constant of G and Planck's Constant h are chosen as a fundamental units then dimension of a mass in a new system​

Answer 1

Answer:

Speed of light C=[LT −1 ]

gravitational constant G=[M −1 L 3 T −2 ]

planck's constant h=ML 2T −1

Let M=C x G y h z

[M]=[LT −1 ] x [M −1 L 3 T −2 ] y [ML 2 T −1 ] z

[M]=[M −y+z L x+3y+2z T −x−2y−z ]−y+z=1,x+3y+2z=0,−x−2y−z=0

On solving, we get

x= 21

;y= 2−1

;z= 21

So, dimension of M=[C 1/2G −1/2 h 1/2 ]