Question

The periodic time $\left(T\right)$ of a simple pendulum of length $\left(L\right)$ is given by $T=2\pi \sqrt{\frac{L}{g}}$. What is the dimensional formula of $T=\sqrt{\frac{g}{L}}$?

• A. $\left[M^0{L}^0{T}^{-1}\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[M^1{L}^1{T}^{-1}\right]$
• D. $\left[M^0{L}^{-1}{T}^1\right]$

Answer 1

The correct option is A $\left[M^0{L}^0{T}^{-1}\right]$

Dimension of $g:\left[M^{0}L{T}^{-2}\right]$

Dimension of $L:\left[M^{0}L\right]$

Now, Dimension of $T\left(\sqrt{\frac{g}{l}}\right):\left[M^0{L}^0{T}^{-1}\right]$