Question

Which one of the following pair of quantities has same dimension?

• A. Force and work done
• B. Momentum and impulse
• C. Pressure and force
• D. Surface tension and stress

Answer 1

The correct option is B

Momentum and impulse

(1) The powers to which the fundamental quantities are elevated in order to express a physical quantity are defined as the dimension of that quantity.

(2) There are a total of seven fundamental dimensions in physics.

(3) Time, mass, and length are the three basic dimensions of mechanics and these are represented by $\left[T\right]$, $\left[M\right]$ and $\left[L\right]$.

(4) As we know impulse $=$change in momentum or $$\begin{gathered} I=∆P \\ =P_f-P_i \end{gathered}$$.

Where $P_f$ is final momentum and $P_i$ is the initial momentum and $I$ is the impulse.

(5) Momentum $=$mass $\times$velocity.

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

So, impulse and change in momentum both have the same dimensions.

Hence the correct option is B.