What is the dimensional formula of time period?

The dimensional formula is defined as the expression of the physical quantity in terms of its basic unit with proper dimensions. The dimensional formula of the time period is given by  [M0L0T1].

The time period is given by the formula:
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].

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