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 $\mathrm{K}$. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is... $\{\mathrm{A}\} 2 \mathrm{~K}$ $\{\mathrm{B}\} \mathrm{K} / 2$ $\{\mathrm{C}\} \mathrm{K} / 4$ $\{\mathrm{D}\} 4 \mathrm{~K}$

Name: Problem 578, Chapter 5: JEE Physics
Uploaded: 2021-10-07T08:49:15-08:00
Duration: 1 min 41 s
Channel: Saman Zulfiqar
Description: 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 doubles. The kinetic energy of the system now is... {A} 2 K {B} K / 2 {C} K / 4 {D} 4 K

   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 $\mathrm{K}$. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is...
$\{\mathrm{A}\} 2 \mathrm{~K}$
$\{\mathrm{B}\} \mathrm{K} / 2$
$\{\mathrm{C}\} \mathrm{K} / 4$
$\{\mathrm{D}\} 4 \mathrm{~K}$

JEE Physics

StemEZ 1st Edition

Chapter 5, Problem 578

Instant Answer

Solved by Expert Saman Zulfiqar

10/07/2021

Step 1

Step 1: The initial kinetic energy of the system is given by $K = \frac{1}{2}I_1\omega_1^2$, where $I_1$ is the initial moment of inertia and $\omega_1$ is the initial angular velocity. Show more…

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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 $\mathrm{K}$. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is... $\{\mathrm{A}\} 2 \mathrm{~K}$ $\{\mathrm{B}\} \mathrm{K} / 2$ $\{\mathrm{C}\} \mathrm{K} / 4$ $\{\mathrm{D}\} 4 \mathrm{~K}$

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Key Concepts

Moment of Inertia

The moment of inertia is a measure of an object's resistance to angular acceleration about an axis. It depends on how the mass of the object is distributed relative to the axis of rotation, with mass further from the axis contributing more to the inertia.

Conservation of Angular Momentum

This principle states that if no external torque acts on a system, its total angular momentum remains constant. In rotational dynamics, when a system's shape changes (such as a varying distribution of mass), the angular velocity adjusts to conserve the overall angular momentum.

Rotational Kinetic Energy

Rotational kinetic energy is the energy an object possesses due to its rotation. It is given by one-half the product of its moment of inertia and the square of its angular velocity. Changes in moment of inertia affect the rotational kinetic energy when angular momentum is conserved.

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