Question

Check the accuracy of the relation `T=2pisqrt((L)/(g))` for a simple pendulum using dimensional analysis.

Answer 1

The dimensional of LHS= the dimension of `T=[M^(0)L^(0)T^(1)]`
The dimension of RHS `=(("dimensions of length")/("dimensions of acceleration "))^(1//2)" "` (`:. 2 pi` is a dimensionless constant )
`((L)/(LT^(-2)))^(1//2)=(T^(2))^(1//2)=[T]=[M^(0)L^(0)T^(1)]`
Since the dimesions are same on both the sides, the relation is correct.