Question

With the usual notations, the following equation $S_n=u+\frac{1}{2}a(2n-1)$ is

• A. only numerically correct.
• B. only dimensionally correct.
• C. both numerically and dimensionally correct.
• D. neither numerically nor dimensionally correct.

Answer 1

Step 1: Given data
Given relation is $S_n=u+\frac{1}{2}a(2n-1)$

Here, u is the initial velocity, a is the acceleration of the body and n is the second in which the distance is covered.

Step 2: Calculation of dimension of the above equation

The dimension of Sn will be $\left[L{T}^{-1}\right]$ as it is the distance covered in 1 sec.

Substitute the dimensions in the equation.

$\left[L{T}^{-1}\right]$ = $\left[L{T}^{-1}\right]$ + $\left[L{T}^{-2}\right]$ $\text{[T]}$

$\left[L{T}^{-1}\right]$ = $\left[L{T}^{-1}\right]$

So, comparing L.H.S and R.H.S dimensionally, on L.H.S $S_n$

Two quantities can be added only if they have the same dimensions. Also, two quantities can be equal only if they have the same dimensions. Hence, the equation is dimensionally incorrect.

Hence the correct option is A