Question

The period T of a simple pendulum is expressed by: √ where ‘l' is the length of the pendulum and ‘g' is the acceleration due to gravity. Show that the formula is dimensionally consistent

Answer 1

Answer:

T = T

Explanation:

The period of a simple pendulum is given by the formula

                           $t = 2\pi \sqrt{\frac{l}{g} }$

Where

                         l - length of the pendulum

                         g - acceleration due to gravity

The dimension of the physical quantities are given by,

                                   t  - T

                                   l - L

                                   g - m/s² - LT⁻²

Substituting in the above equation,

                                T = 2π √(L / LT⁻²)

Considering only the dimensional units in the equation

                                 T = √(L / LT⁻²)

                                  T = T

This shows that the formula for a simple pendulum is dimensionally consistent, T = T