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find the expression for cenripetal force F =mrw 2 by dimensional method.

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2 years ago

```							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.Let F = km a v b r c … (i)Where, k is the dimensionless constant of proportionality, and a, b, c are the powers of m, v, r respectively.On writing the dimensions of various quantities in (i), we get[M 1 L 1 T −2 ] = M a [LT −1 ] b L c= M a L b T −b L cM 1 L 1 T −2 = M a L b + c T −bOn applying the principle of homogeneity of dimensions, we geta = 1,b= 2,b + c = 1 …(ii)From (ii), c = 1 − b = 1 − 2 = −1On putting these values in (i), we getF = km 1 v 2 r −1OR F = k mv^2 / r ORF = k* mrw^2This is the required relation for centripetal force.
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2 years ago
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