Question
Sat June 23, 2012 By:

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Expert Reply
Sat June 23, 2012
dimension of physical quantities used are:
Mass,m:                  [M]
Radius,r:               [L]
Angular velocity,?: [T-1]
Force,F:                 [MLT-2]
 
Let the formula for centripetal force be:
 
F = kmarb?c
Here k is a dimensionless constant
So dimensionally it will look like:
[MLT-2] = [M]a [L]b [T-1]c
[MLT-2] = [M]a [L]b [T]-c
 
comparing the powers of both sides we get:
a =1
b = 1
c = 2
 
thus dimensionally the formula would be:
 
F = kmr/?2
 
what we actually do in dimension analysis is we compare the dimensions on bith sides and check and modify them to make them equal otherwise the units on both the sides will be unequal
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