First slide

Dimensions of physical quantities

Question

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

Moderate

A

Only numerically correct
B

Only dimensionally correct
C

Both numerically and dimensionally correct
D

Neither numerically nor dimensionally correct

Solution

We can derive this equation from equations of motion. So it is numerically correct.
$\begin{matrix} S_{t} = Distance travelled in t^{th} second = \frac{Distance}{Time} = [L] \\ u = Velocity = [L T^{- 1}] and \frac{1}{2} a (2 t - 1) = [L T^{- 1}] \end{matrix}$
As dimensions of all terms in the given equation are not same, hence equation is not dimensionally correct.

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