Question

Obtaining the relationship between quantities using method of dimensions: The centripetal force (F) acting on the body is assumed to depend on the mass (m) of the body, it's linear velocity (v) and radius of circular path (t) Hence show that F=k~mv^{2}/r~bi using method of dimensions. Here k is a constant of proptionality​

Answer 1

Explanation:

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

[MLT2]=[M]x[LT−1]y[L]z=[MxLy+zT−y]

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

x=1,y=2andy+z=1

or z=1−y=−1

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

F=kmv2r−1=krmv2

F=rmv2 (where k=1)