Question:

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is KK. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is

Updated On: Dec 5, 2023
  • 2K2K
  • K2\frac{K}{2}
  • K4\frac{K}{4}
  • 4K4K
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The Correct Option is B

Solution and Explanation

According to the principle of conservation of angular momentum,
IωI \omega = constant
As II is doubled, w becomes half.
Now K.E. of rotation, K=12Iω2K = \frac{1}{2} I \omega^2
Since II is doubled and ω\omega is halved, therefore
K.E. will become half i.eK2i.e \frac{K}{2}
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Concepts Used:

System of Particles and Rotational Motion

  1. The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
  2. The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
  3. The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.