According to the provided information , `F prop m^(a) v^(b) r^( c ) `
rArr `F = km^(a) v^(b) r^(c ) ` ….(i)
Where `k` is the dimensionless constant of proportionality and `a , b, c` are the constant powers powers of `m , v , r`, respectively.
Now using the principle of homogenity , comparing the power of like quantities on both the sides , we have
` a = 1 ( ii) b + c = 1 (iii) and b = 2 (iv)
Using (ii) , (iii) , and (iv) , we have a = 1 , b = 2 , and `c = -1`.
Using (ii) , (iii) , and (iv), we have ` a = 1 , b = 2 , c = -1`.
Using these values in (i) , ` F = km^(1) v^(2) r ^(-2)`
`implies F = K (mv^(2))/(r)` which is the desired relation.
