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

We need to find the dimensional formula of angular impulse.

Concept Used:

Angular impulse is defined as the product of torque and time. Torque is the rotational analogue of force, given by \( \vec{\tau} = \vec{r} \times \vec{F} \). The dimensional formula can be derived from this relationship.

Step-by-Step Solution:

Step 1: Write the definition of angular impulse.

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

Step 2: Find the dimensional formula of torque.

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

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

The dimensional formula of force is \( [M L T^{-2}] \), and distance is \( [L] \).

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

Step 3: Find the dimensional formula of time.

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

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

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

Thus, the dimensional formula of angular impulse is [M L² T⁻¹].