Question

Obtain an expression for the time period T of a simple pendulum. The time period T depends on 

1. Mass of the bob(m) 

2. Length of the pendulum (l) 

3. Acceleration due to gravity (g) at the place where the pendulum is suspended, 

(constant k = 2π)

Answer 1

Example: 

An expression for the time period T of a simple pendulum can be obtained by using this method as follows. 

Let true period T depend upon

1. Mass m of the bob 

2. Length l of the pendulum and

3. Acceleration due to gravity g at the place where the pendulum is suspended. Let the constant involved is k = 2π.

Here k is the dimensionless constant. Rewriting the above equation with dimensions.

Comparing the powers of M, L and T on both sides, a = 0, b + c = 0, -2c = 1 

Solving for a, b and c ⇒ a = 0, b = 1/2, and c = -1/2 

From the above equation

Experimentally k = 2π, hence

T = 2π \(\sqrt {l/g}\)