Question

derive a relation of time period of a simple pendulum using dimensional analysis​

Answer 1

The dimensional formula of Time Period is given by,

[M0 L0 T1]

Where,

M = Mass

L = Length

T = Time

Derivation

Time Period (T) = 2× π × √(L/g) . . . . . (1)

Where, L = length of string and g = Acceleration due to gravity

The dimensional formula of length = [M0 L1 T0] . . . . (2)

And, the dimensional formula of accleration due to gravity = [M0 L1 T-2] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Time Period (T) = 2× π × √(L/g)

Or, T = √[M0 L1 T0] × [M0 L1 T-2]-1 = √[T2] = [M0 L0 T1].

Therefore, the time period is dimensionally represented as [M0 L0 T1]. hope it helps u