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If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen
as fundamental units, then the dimensions of mass in new system is
 

Asked by shambhavirai 7th June 2016, 7:52 AM
Answered by Expert
Answer:

Hi Shambhavirai,

The dimensions for velocity are:

[c] = [L][T]-1

Similarly, the dimensions for Planck's constant are:

[h] = [M][L]2

And, the dimensions for Gravitational constant are:

[G] = [M]-1 [L]3 [T]-2

Hence, the dimensions of mass will be

begin mathsize 12px style open square brackets straight M close square brackets equals straight h open square brackets straight L close square brackets to the power of negative 2 end exponent equals straight h open parentheses fraction numerator hG over denominator straight c 2 end fraction close parentheses to the power of negative 2 over 3 end exponent
open square brackets straight M close square brackets equals open square brackets straight h close square brackets to the power of 1 third end exponent open square brackets straight G close square brackets to the power of negative 2 over 3 end exponent open square brackets straight c close square brackets to the power of 4 over 3 end exponent end style

Answered by Expert 20th June 2016, 6:02 PM
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