Question

Suppose you design your system of dimensions and take velocity (V), Planck constant (h) and gravitational constant (G) as the fundamental quantities. What will be the dimensions of length (L), mass (M) and time (T) in this system ?
Explain Briefly ​

Answer 1

Let l∝c

x

h

y

G

z

;l=kc

x

h

y

G

z

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

Equating dimensions on both sides, we get

[M^0LT]=

[LT^-¹]^x[ML²T^-¹]^y[M^-¹L³T^-²]^z

=[M^y-zL^x+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= 2/1

z= 2/1

∴

1=√Hg/c³

hope it helps....

not copied from anywhere...

Answer 2

Answer:

Hope the attached images helps you to find out the answer..