The force F acting on a body moving in a circular path depends on mass of the body (m) velocity(v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method (k=1)

The force F acting on a body moving in a circular path depends on mass

1.	The force F acting on a body moving in a circular path depends on mass of the body (m) velocity(v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method (k=1)
Answer» SOLUTION :The PRINCIPLE of homogeneity of DIMENSIONS states that the dimensions of all the termsin a physical expression should be the same. For example, in the physical expression `v^2= u^2 + 2as` , the dimensions of `v^2 , u^2` and 2 as are the same and equal to `[L^2 T^(-2) ]` ` F prop m^a v^b R^c` `F = K m^z v^b r^c `K = 1 ` F= m^a v^b r^c` Dimensionally `[MLT^(-2) ] = [M]^a [LT^(-1) ]^b [L]^c` Campare the power of M,L and T a = 1...(1) b + c= 1....(2) - b= - 2 b = 2....(3) sub (3) and (2) we get b+c=1 2 + c = 1 c = -1.....(4) Substitute a, b and c value in force equation `F = m^a v^b r^c` ` = mv^2 r^(-1)` `F = (mv^2)/(r )` This equation is known as centripetal force.