Answer :

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 = cahbGc, 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 = cahbGc, 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 = cahbGc, 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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