find the powers p and q required for dimensional consistency.?
To find the powers p and q necessary for dimensional consistency, let's consider the period T of a simple pendulum. The period is defined as the time taken for the pendulum to complete one full oscillation. If we denote the length of the pendulum as L and the acceleration due to gravity as g, T can be expressed by the equation T = 2π L^p g^q. Please help determine the values of p and q that ensure this equation maintains dimensional consistency.
1 Answers
T is in seconds or units of time.
L is in length
g is in length*time^(-2)
So L^p g^q has units (length)^p (length)^q *(time)^(-2q)
= (length)^(p+q) * (time)^(-2q)
This has to be equal to (time).
That tells you p+q = 0 since there's no length units on the left hand side
And -2q has to be equal to 1. So that tells you q, which tells you what p has to be.
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