a particle of mass m is tied in a string and is swung around in a circular path of radius r with a constant speed v . Derive a formula for the centripetal force F exerted by the particle on our hand , using the method of dimensions.

F = k m^a* r^b* v^c
[M L T^-2] = k [ M^a] [ L^b] [L T^{- 1}]^c
[M L T^-2] = K [M^a L^b+c  T^{- c}]^​
a=1                                                  (1)
-c=-2                                                (2)
so, c=2
b + c = 1                                         (3)
b+2=1
b=1-2
so,b=-1
now yhe value of a, b and c=
a=1,b=-1,c=2
F= k m¹ r^-1 v²
k = 1
so, the equation comes out to be =
F = mv²/r.