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derive the expression for time period of a simple pendulum as T = 2pi * root l/g by dimensional analysis.

derive the expression for time period of a simple pendulum as T = 2pi * root l/g by dimensional analysis. 

Grade:10

1 Answers

Arun
25763 Points
2 years ago
You need to remember the formula of constant of simple pendulum such that:
k = L/T^2
You need to consider the value of constant equivalent to g/(4pi^2) (g expresses the gravity acceleration)
You need to set the equations g/(4pi^2) and L/T^2 equal such that:
L/T^2 = g/(4pi^2)
You need to find time period such that:
g*T^2 = 4pi^2*L
T^2 = (4pi^2*L)/g => T = 2pi*sqrt(L/g)
Hence, evaluating the time period of simple pendulum under given conditions yields T = 2pi*sqrt(L/g).

 

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