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Grade: 10

                        

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

2 years ago

Answers : (1)

Arun
25236 Points
							

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 c

M 1 L 1 T −2 = M a L b + c T b

On applying the principle of homogeneity of dimensions, we get

a = 1,

b= 2,

b + c = 1 …(ii)

From (ii), c = 1 − b = 1 − 2 = −1

On putting these values in (i), we get

F = km 1 v 2 r −1

OR

 

F = k mv^2 / r

 

OR

F = k* mrw^2

This is the required relation for centripetal force.

2 years ago
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