Question

A sphere of radius 'a' moves with velocity 'v' in a medium and the force 'f' actung on it is given by f=Gπav, where 'a' is acceleration, 'v' velocity and 'k'-ax unknown physical quantity. Find dimension of R

Answer 1

Answer:

We know that ,

[F]=[MLT−2],[V][M0LT−1],

[A]=[LT−2] and [L]=[ML2T−1]

WhereLis the angular momentum 

let [L]=[F]a[V]b[A]c  

⇒[ML2T−1]=[MLT−2]a[LT−1]b[LT−2]c

⇒[ML2T−1]=[M(a)L(a+b+c)T(−2a−b−2c)]

By analysing , we get

a=1

a+b+c=2

2a+b+2c=1

By solving these equations , we get 

a