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Power P =
Work / Time = Force * distance/ TIme
= mass * accelaration * distance/Time
= mass * (distance/time2) * distance/time
= mass * distance3 * time-3
Therefore, [P] = [ML3T-3]
Let mass M be PxLyTz .
Hence, M = [ML3T-3]xLyTz = MxL(3x+y)T(-3x+z)
Write the LHS as M1L0T0. Then, by comparing the exponents on both sides, we get 3 equations :
x = 1..............(1)
3x+y = 0................(2)
-3x+z = 0...................(3)
Using (1) in (2), y = -3
Using (1) in (3), z=3.
Therefore, M = P1L-3T3
Hi
units of P = W = kg.m^2/s^3 L = m T = s
For getting the dimensional formula for mass (kg) assume : P^p L^l T^t = kg
putting the units in place of P, L and T (kg.m^2/s^3)^p m^l s^t = kg Comparing the units on LHS and RHS : (for kg) p=1 (for s) -3p+t = 0 t = 3p = 3 (for m) 2p + l=0 l = -2p = -2
Then we get the formula as : [P] [L]^-2 [T]^3 = kg
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