Question

7. The Centripetal force acting on a body depends upon the mass m of the particle , its velocity v and radius r of the circle. Derive the relation among the physical quantities dimensionally?

Answer 1

Let F=k(m)^x (v)^y (r)^z

Here, k is a dimensionless constant of proportionality. Writing the dimensions of RHS and LHS in Eq. (i), we have

[MLT^2]=[M]^x [LT^−1]^y [L]^z =[M^x L^y+z T^−y]

Equation the powers of M, L and T of both sides, we have,

x=1 y=2 & y+z=1

or z=1-y=-1

Putting the values in Eq. (i), we get

F=kmv^2r^-1 =k×mv^2/r

F=mv^2/r (where k=1)

Hope it is helpful...:)