Question

In the equation $S_{nth}=u+\frac{a}{2}(2n-1)$, the letters have their usual meanings. The dimensional formula of $S_{nth}$ is

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

Answer 1

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

The Dimensional Formula of $S_{nth}$ is same as that of the Dimensional formula of $u$ (2 variables with same units can be added)

So Dimensional Formula of $S_{nth}$ = DImensional Formula of $u$ = $\left[M^{0}L{T}^{-1}\right]$