Question

The dimensional formula of angular impulse is :

• A. [M L^–2 T^–1]
• B. [M L² T^–2]
• C. [M L T^–1]
• D. [M L² T^-1]

Answer 1

The Correct Option is D

Determine the dimensional formula for angular impulse.

Concept Used:

Angular impulse equals torque multiplied by time. Torque, the rotational equivalent of force, is defined as \( \vec{\tau} = \vec{r} \times \vec{F} \). This relationship allows for deriving the dimensional formula.

Step-by-Step Solution:

Step 1: State the definition of angular impulse.

\[\text{Angular Impulse} = \text{Torque} \times \text{Time}\]

Step 2: Establish the dimensional formula for torque.

Torque (\( \tau \)) = Force × Perpendicular Distance

\[[\text{Torque}] = [\text{Force}] \times [\text{Distance}]\]

The dimensions for force are \( [M L T^{-2}] \) and for distance are \( [L] \).

\[[\text{Torque}] = [M L T^{-2}] \times [L] = [M L^2 T^{-2}]\]

Step 3: Determine the dimensional formula for time.

\[[\text{Time}] = [T]\]

Step 4: Combine the dimensions to derive the dimensional formula for angular impulse.

\[[\text{Angular Impulse}] = [\text{Torque}] \times [\text{Time}] = [M L^2 T^{-2}] \times [T] = [M L^2 T^{-1}]\]

Consequently, the dimensional formula for angular impulse is [M L² T⁻¹].