Question

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

Answer 1

Hey mate here is your

Answer:

[m]=c12G−12h12

Explanation:

Here, [c]=LT−1 

[G]=M−1L3T−2

[h]=M1L2T−1

Let mαcxGyhz

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

M=(LT−1)x(M−1L3T−2)y(ML2T−1)z

M=[My+zLx+3y+2zTx−2y−z]

By equating the power of M, L, T in both the sides:

−y+z=1,x+3y+2z=0,−x−2y−z=0

By soling the above equation ,

We get, 

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