Question

Using dimensional analysis obtain an expression for centripetal force​

Answer 1

Answer:

The centripetal force, F acting on a particle moving uniformly in a circle depend upon the mass (m), velocity (v) and radius (r) of the circle. The formula for F using the method of dimensions. Where, k is the dimensionless constant of proportionality, and a, b, c are the powers of m, v, r respectively

Answer 2

Answer:

a=1; b=2; c=-1

Explanation:

We have: F=M, V, R.

Let F = k×M^a×V^b×R^c ... <1> (~k=constant)

now; Dimensional formula of LHS;

F=[M^1×L^1×T^-2] ...<2>

&Dim. formula of RHS;

M^aV^bT^c = [M]^a×[LT^-1]^b×[L]^c

=> [M^aL^bT^-bL^c]

=> [M^aL^b+cT^-b] ... <3>

on comparing <2>&<3>...

{a=1}; b+c=1... <4>

{-b= -2}=> {b=2};

put b=2 in <4>...

{c=-1}

so a=1; b=2; c=-1

now put the value of a, b, &c in eq. <1>

F=k×[M^1V^2R^-1]

=>F=k MV^2/r (where k is constant).