Question

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

• A. \( [M L^2 T^{-2}] \)
• B. \( [M L^2 T^{-4}] \)
• C. \( [M L^2 T^{-3}] \)
• D. \( [M L^2 T^{-1}] \)

Hint:

When multiplying physical quantities, combine their dimensional formulas. Moment of inertia and angular velocity have the respective dimensional formulas \( [M L^2] \) and \( [T^{-1}] \). Squaring angular velocity gives \( T^{-2} \).

Answer 1

The Correct Option is B

Moment of inertia \( I \) has the dimensional formula: \[ I = [M L^2] \] Angular velocity \( \omega \) has the dimensional formula: \[ \omega = [T^{-1}] \] The dimensional formula of the product of moment of inertia and square of angular velocity is: \[ I \cdot \omega^2 = [M L^2] \cdot [T^{-2}] = [M L^2 T^{-2}] \]
Thus, the dimensional formula is \( [M L^2 T^{-4]} \).