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The contripetal force F acting on a part...

The contripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and redio ( r) of the circle . Derive the formula for F using the method of dimensions.

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Let `F = k(m)^(x) (v)^(y) ( r)^(z)` ..(i)
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^(z) L^(y+z)T^(-y)] `
Equating the power of M,L and T of both side , we have ,
`x= 1, y= 2, and y+z= 1 or z= 1-y = -1`
Puting the value in Eq , (i) we gwt
`F = kmv^(2)(r^(-1)) = k(mv^(2))/(r)`
or `F= (mv^(2))/(r)` (where`k=1`)
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