Obtain an expression for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r . Take dimensionless constant K = 1 .

Explanation

Consider centripetal force `F= km^(a)v^(b)r^(c )`, here k is proportionally constant and is dimensionless.
Equating for dimensions on both the sides, we get
`M^(1)L^(1)T^(-2)= [M]^(a)[LT^(-1)]^(b)[L]^(c )`
`=M^(a)L^(b+c)T^(-b)`
Comparing the exponents of M, L and T on both sides, we get
`a= 1, b+c= 1 " and "b=2`
`implies c= 1-2=1`
`F= (mv^2)/(r )`
This is the required expression for centripetal force.