A body of mass m is moving in a circle of radius r with angular velocity `omega`. Find an expression for the centripetal force f acting on it using method of dimensional analysis.

Explanation

Let `F propm^(a)r^(b)omega^(c )impliesF=km^(a)r^(b)omega^(c )`.................(i)
Where k is dimensionless quantity
Substituting the dimensional formula of the various quantities, we have
`MLT^(-2)=M^(a)L^(b)(T^(-1))^(c )`
Comparing the dimension on both sides, we have
`a=1`, `b=1` and `-c=2implies c=2`
Substituting in (i), we get `F=kmromega^(2)`.