Dimensional Analysis Making new formula - 2

Description:

A particle of mass `m` is moving in circular path with constant speed `V` and radius `r`. Find expression of its centripetal force F.

Solution

To form a new formula we will use dimensional analysis.

Step 1 − Write the relation with assumed powers and an arbitrary constant.

F = km^a V^b r^c

Where,

F = Centripetal force

k = Arbitrary constant

m = Mass of particle

V = Speed of particle and

r = radius of circular path.

Step 2 − Writing dimensions of each quantity.

M¹ L¹ T^-2 = [M]^a [L T^-1]^b [L]^c

M¹ L¹ T^-2 = [M]^a [L]^b+c [T]^-b

Step 3 − Compare similar dimensions.

After comparing similar dimensions, we get −

a = 1, b + c = 1, -b = -2

a = 1, b = 2, c = -1

Step 4 − Substitute the power of dimensions in the equation formed in step 1.

F = km V² r^-1

F = km V²/r