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 $K$. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is
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 $K$. 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
- $2K$
- $\frac{K}{2}$
- $\frac{K}{4}$
- $4K$
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The Correct Option is B
Solution and Explanation
According to the principle of conservation of angular momentum,
$I \omega $ = constant
As $I$ is doubled, w becomes half.
Now K.E. of rotation, $K = \frac{1}{2} I \omega^2$
Since $I$ is doubled and $\omega$ is halved, therefore
K.E. will become half $i.e \frac{K}{2}$
$I \omega $ = constant
As $I$ is doubled, w becomes half.
Now K.E. of rotation, $K = \frac{1}{2} I \omega^2$
Since $I$ is doubled and $\omega$ is halved, therefore
K.E. will become half $i.e \frac{K}{2}$
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Concepts Used:
System of Particles and Rotational Motion
- 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.
- 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.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.