The periodic time (T) of a simple pendulum of length (L) is given by `T=2pisqrt((L)/(g))`. What is the dimensional formula of `Tsqrt((g)/(L))`?

Options

A. `[M^(0)L^(1)T^(0)]`
B. `[M^(0)L^(0)T^(0)]`
C. `[M^(1)L^(1)T^(-1)]`
D. `[M^(0)L^(-1)T^(1)]`

Answer

b

Explanation

`because T=2pisqrt((L)/(g)) therefore (T)/(sqrt((L)/(g)))=Tsqrt((g)/(L))=2pi`
But `2pi` is a constant and it has the dimensions of `M^(0)L^(0)T^(0)`
`therefore` The dimensional formula for `Tsqrt((g)/(L))` is `[M^(0)L^(0)T^(0)]`