If the fundamental quantites are velocity `(upsilon)`, mass (M), time (T), what will be the dimensions of `eta` in the equaiton `V = (pi pr^4)/(8I eta)` where the symbosl have their usual meaning?

Answer

`M^1 upsilon^(-1) T^(-2)`

Explanation

From `V =(pi)/(8) (pr^4)/(I eta)`
`eta =(pi)/(8)(pr^4)/(IV) where V = volume//sec = [L^3 T^(-1)]`
`eta = ([ML^(-1)T^(-2)][L^4])/(L[L^3 T^(-1)]) = [M^1L^(-1) T^(-1)]`
As `upsilon =("dinstance")/("time") =(L)/(T) , L =upsilon T`
`:.eta =ML^1 (upsilonT^(-1))T^(-1) =[M^1 upsilon^(-1) T^(-2)]`