Correct Answer - Option 2 : [M
1L
2T
-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]