The buoyant force `F` acting on a body depends on the density of medium `rho`, volume of body immerese `V` and acceleration due to gravity `g`. Establish the relation using method of dimensions.

Explanation

`F = fn (rho, V, g)`
`F prop rho^(a) V^(b) g^(c )`
`[MLT^(-2)] prop [ML^(-3)]^(a) [L^(3)]^(b) [LT^(-2)]^(c )`
`M^(1) L^(1) T^(-2) prop M^(a) L ^(-3a + 3b + c) T^(-2c)`
Comparing power of `M, L` and `T`,
`a = 1`
`- 3 a + 3 b+ c = 1`
`- 2c = - 2`
`a = 1, b = 1, c = 1`
`F prop rho v g implies F = k rho Vg`
From experiments, `k = 1`
`F = rho Vg`