Question

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 1

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.