A body of mass m moves in a circular path of radius r with a velocity v. Find the expression for the centripetal force F acting on the body by using method of dimensions.

Explanation

Let `Fpropm^(a)r^(b)v^(c )`
`implies F= km^(a)r^(b)v^(c )`…………(i)
Where k is dimensionless constant.
Substituting the dimensional formulae of various quantities , we have
`MLT^(-2)=M^(a)L^(b)(LT^(-1))^(c )` or `MLT^(-2)=M^(a)L^(b+c)T^(-c)`
Comparing powers on both sides, we get
`a=1`, `b+c=1`, `-c=-2` or `a=1` , `c=2` and `b=-1`
Substituting in (i) we have `F=k(mv^(2))/(r )`