Question

The dimensional formula for the product of moment of inertia and the square of angular velocity is

• A. \(MLT^{-2}\)
• B. \(ML^{2}T^{-1}\)
• C. \(ML^{0}T^{-2}\)
• D. \(ML^{2}T^{-2}\)
• E. \(MLT^{-1}\)

Hint:

Rotational kinetic energy = \(\frac{1}{2} I \omega^2\) has dimensions of energy \(ML^2T^{-2}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Moment of inertia \(I\) has dimensions \(ML^2\). Angular velocity \(\omega\) has dimensions \(T^{-1}\).

Step 2: Detailed Explanation:
\(I \cdot \omega^2\) has dimensions: \([ML^2] \cdot [T^{-1}]^2 = ML^2 T^{-2}\)
This is the dimensional formula for rotational kinetic energy.

Step 3: Final Answer:
\(ML^{2}T^{-2}\).