Question

if the velocity of light c,coefficient of viscosity gravitational constant are taken as fundamental quantities then the expression of mass m in terms of dimensions of these quantities is proportional to_____​

Answer 1

Answer:

Let l∝cxhyGz;l=kcxhyGz

where k is a dimensionless constant and x, y and z are the exponents.

Equating dimensions on both sides, we get

[M0LT0]=[LT−1]x[ML2T−1]y[M−1L3T−2]z

=[My−zLx+2y+3zT−x−y−2z]

Applying the principle of homogeneity of dimensions, we get

y−z=0                         ....(i)

x+2y+3z=1                 ....(ii)

−x−y−2z=0                  ...(iii)

On solving Eqs. (i), (ii) and (iii), we get

x=2−3,y=21z=21∴l=c3hG

Answer 2

Answer:

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