The period

T

of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is

L

and the acceleration of gravity is

g

,

then

T

is given by

T

=

2

π

L

p

g

q

.

Find the powers

p

,

q

required for dimensional consistency.

Answer: p = - {1/2}, q = {1/2}

Explanation: The frequency of oscillation of a pendulum is given as

F = 1/2π * √{l/g}

Where √ is square root

l is lenght

g is acceleration due to gravity

But

F = 1/T

Where T is the period of Oscillation

Making T subject of formula we have

T = 1/F

T = 2π√{g/l}

Here the power on l is - [1/2] = p

Also,

Power on g is 1/2 = q

All because of the square root.