# The dimensional formula of rotational kinetic energy is-

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The dimensional formula of rotational kinetic energy is-
1. [M1L-1T-2]
2. [M1L2T-2]
3. [M2L2T-3]
4. [M1L4T-2]

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Correct Answer - Option 2 : [M1L2T-2]

The correct answer is option 2) i.e. [M1L2T-2]

CONCEPT:

• Rotational kinetic energy: Rotational kinetic energy is due to the motion of an object's rotation.

For a given fixed axis of rotation, the rotational kinetic energy is given by:

$KE = \frac{1}{2} Iω^2$

Where I is the moment of inertia, ω is the angular velocity.

EXPLANATION:

Rotational kinetic energy$KE = \frac{1}{2} Iω^2$

• The SI unit of angular velocity ω is rad/s.
• Radian is a dimensionless quantity.
• Hence, the base unit of ω is s-1.
• Thus, its dimension is [T-1].
• Moment of inertia, I = Mr2 where M is the mass and r is the radius.
• Thus, its dimension is [M1L2T0].
• Therefore, the dimensions of rotational kinetic energy = [M1L2T0] × [T-1]2 = [M1L2T-2]