The viscous force `F_(v)` acting on a small ball of radius `r` moving in medium of coefficient of viscosity `eta` with speed `v` is proportional to `eta^(a) r^(b) v^(c )`. Find the values of a, b and c.

Explanation

`F_(v) prop eta^(a) r^(b) v^(c )`
`[MLT^(-2)] prop [ML^(-1) T^(-1)]^(a) [L]^(b) [LT^(-1)]^(c )`
`M^(1) L^(1) T^(-2) prop M^(a) L^(-a + b + c) T^(-a -c)`
Comparing powers of `M, L` and `T`
`a = 1`
`-a + b + c = 1`
`-a - c = - 2`
From (i) and (iii), `c = 1`
`-a + b + c = 1`
`-1 + b + 1 = 1 implies b = 1`
`a = 1, b = 1, c = 1`