INDIGO BOOK DOUBT

I was reading the Indigo book. On page number 25, under the topic DIMENSIONAL ANALYSIS, I could not understand one reason during the explanation of the example of DERIVATION OF A FORMULA. Please elaborate the BOLD and UNDERLINED part. The example was as follows:

EXAMPLE: The time period of a Simple Pendulum (T)
We assume that T depends on the following factors:
Mass of the bob, m; Effective length of the Pendulum, l; Acceleration due to gravity, g
Let T = malbgc
[M0L0T] = [ML0T0] a X [M0LT0]b X [M0LT-2]c
Comparing the powers of each of the dimensions on both sides we can derive a relationship.
M0 = Ma+0+0............................ (=> a=0, hence T is independent of the Mass of the bob)
L0 = L0+b+c.......................... (=> b + c = 0)
T1 = T0+0-2c...................... (=> -2c =1, hence T α 1/√c )
Using b + c =0 and c = -1/2, we can say b = ½
Therefore, T = k√(l/g) where k is a dimensionless constant.

1 Answers

1
Kalyan Pilla ·

Well, it is supposed to be T α 1/√g , if that is what is ur doubt!!

Your Answer

Close [X]