Question

If the fundamental quantities are velocity , mass (m) and time (T), what will be the dimensions of in the equation V= 8 4 ?​

Answer 1

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Let M = (some Number) (V)ª (F)¹ (T) Equating dimensions of both the sides M1LT0 = (1)[LT1]$\rm{ [ML^{1}T^{-2}][T] M^{1}LOT }$

$\rm{ = M^{b}L^{a+b}T^{-a}-2^{b+c} }$

get a = -1, b = 1, c = 1

M = (Some Number) (V-¹F¹T¹)

[M] = [V-¹F¹T¹]

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Similarly, we can also express energy in terms of V, F, T

Let [E] = [some Number] [V]ª[F] [T] [ML²T2] = [MºLºTº][LT-¹]ª[MLT-2]¹[T]c

$\rm{ [M^{1} L^{2} T^{2} ] = [M^{1} L^{b}+b^{T-a}-2^{b+c}] }$

$\rm{ → 1 = b; 2 = a +b; -2=-a-2b + c }$

get a = 1; b= 1; c= 1

E = (some Number) $\rm{ V^{1}F^{1}T^{1}or [E] = [V^{1}][F^{1}][T^{1}] }$

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