Question

$MLT^{-1}$ is the dimensional formula for

• A. Speed
• B. Acceleration
• C. Impulse
• D. Force

Hint:

Remember the Impulse-Momentum Theorem: Impulse is equal to the change in momentum. Since they are physically equivalent in terms of effect, they must share the same dimensional formula, $[MLT^{-1}]$.

Answer 1

The Correct Option is C

Let us analyze the dimensional formulas for all the provided options to identify the correct match. 1. Speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{[L]}{[T]} = [LT^{-1}]$.

2. Acceleration: $\text{Acceleration} = \frac{\text{Velocity}}{\text{Time}} = \frac{[LT^{-1}]}{[T]} = [LT^{-2}]$.

3. Force: $\text{Force} = \text{Mass} \times \text{Acceleration} = [M] \times [LT^{-2}] = [MLT^{-2}]$.

4. Impulse: Impulse is defined as the product of Force and Time ($J = F \cdot \Delta t$) or change in Momentum ($p = mv$). $$\text{Impulse} = [MLT^{-2}] \times [T] = [MLT^{-1}]$$ Alternatively, $\text{Momentum} = [M] \times [LT^{-1}] = [MLT^{-1}]$. As per the analysis, $MLT^{-1}$ corresponds to Impulse (and Linear Momentum).