Question

Show that the expression of the time period $T$ of a simple pendulum of length $l$ given by $T=2\pi \sqrt{\frac{l}{g}}$ is dimensionally correct.

• A. As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct.
• B. The dimension of LHS and RHS are not same
• C. It cannot be solved
• D. None of these

Answer 1

Answer: (A)

As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct.

$T=2\pi \sqrt{\frac{l}{g}}$

Dimensionally $\left[T\right]=\sqrt{\frac{\left[L\right]}{\left[L{T}^{-2}\right]}}=\left[T\right]$

As in the above equation, the dimensions of both sides are same. The given formula is dimensionally correct.