Assignment 1.7: Find an expression for the time period T of a simple pendulum. The time period may depend upon (i) mass m of the bob of the pendulum, (ii) length l of pendulum, (iii) acceleration due to gravity g at place where the pendulum is suspended.

Solution

Given that the time period T depends upon the mass of the bob, length of the pendulum and ‘g’. Let the relation is

In terms of dimensions, the equation will be

Now the powers of the same quantities on both sides must be equal.

For M, a = 0 — (1)

For L, b + c = 0 — (2)

For T, -2c = 1 ⇒ c = – ½ — (3)

Put this value of c in equation (2), b – ½ = 0 ⇒ b = ½ (4)

Now substitute these values in equation (A)

Where the experimentally calculated value of k = 2π.