Question

In `CGS` system the magnitude of the force is 100 dynes. In another system where the fundamental phyical quamtities are kilogram , meter , and minute, find the magnitude of the force.

Answer 1

We have `n_(1) = 100 , M_(1) = g , L_(1) = cm , T_(1) = s and M_(2) = kg , L_(2) = m ,T_(2) = min`, the dimensional formula of forces is `[M^(1) L^(1) T^(2)]`.
Where `a = 1 , b = 1 , c = -2`.
By substituting these values in the following conversion formula,
we have
`n_(2) = n_(1) [(M_(1))/(M_(2))]^(a) [[(L_(1))/(L_(2))]^(b)[(T_(1))/(T_(2))]^(c)`
` = 100 [ (g)/(kg)]^(1) [ (cm)/( m)]^(1) [( s)/( min)]^(-2)`
`= 100[(g)/(10^(3)g)]^(1) [(cm)/(10^(2) cm)]^(1) [ (s)/( 60 s)]^(-2) = 3.6`