find the powers p and q required for dimensional consistency.?

the period T of a simple pendulum is the amount of time required fot it to undergo one complete oscillation. if the lenght of the pendulum is L and the acceleration of gravity is g, then T is given by, T = 2Pi L^p g^q

1 Answer

  • 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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