If velocity of li

The dimensional formula for velocity of light c is [M⁰L¹T^-1], for plank’s constant h is [ML²T^-1] and for gravitational constant G is [M^-1L³T^-2].

1. Let the dimensional formula for mass m = c^ah^bG^c, then substituting the dimensional formula for c, h and G we have

Equating the exponents of like quantities on both sides we have

Adding the three equations and solving for b we have

Using this value of b and substituting in the above equations, we have

Now, substituting these equations in the expression for mass m we have

2. Let the dimensional formula for length l = c^ah^bG^c, then substituting the dimensional formula for c, h and G we have

Equating the exponents of like quantities on both sides, we have

Adding the three equations and solving for b we have

Using this value of b and substituting in the above equations, we have

Now, substituting these equations in the expression for length l we have

3. Let the dimensional formula for time t = c^ah^bG^c, then substituting the dimensional formula for c, h and G we have

Equating the exponents of like quantities on both sides, we have

Adding the three equations and solving for b we have

Using this value of b and substituting in the above equations, we have

Now, substituting these equations in the expression for length l we have