Answer :

The dimensional formula for velocity of light c is [M^{0}L^{1}T^{-1}], for plank’s constant h is [ML^{2}T^{-1}] and for gravitational constant G is [M^{-1}L^{3}T^{-2}].

1. Let the dimensional formula for mass m = c^{a}h^{b}G^{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^{a}h^{b}G^{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^{a}h^{b}G^{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

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