Question

A child is standing with folded hands at the centre of a plattorm rotating about its central axis, The kinetic energy of the system is $K$. Now, the child stretches his arms so that moment of inertia of the system doubled. Now, the kinetic energy of the system is (a) $\frac{K^{}}{4}$ (b) $\frac{K}{2}$ (c) $2 \mathrm{~K}$ (d) $4 K^{}$

Name: Problem 82, Chapter 7: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T14:38:27-08:00
Duration: 2 min 58 s
Channel: Dheeraj Sharma
Description: A child is standing with folded hands at the centre of a plattorm rotating about its central axis, The kinetic energy of the system is K. Now, the child stretches his arms so that moment of inertia of the system doubled. Now, the kinetic energy of the system is (a) (K^*)/(4) (b) (K)/(2) (c) 2 K (d) 4 K^*

   A child is standing with folded hands at the centre of a plattorm rotating about its central axis, The kinetic energy of the system is $K$. Now, the child stretches his arms so that moment of inertia of the system doubled. Now, the kinetic energy of the system is
(a) $\frac{K^{*}}{4}$
(b) $\frac{K}{2}$
(c) $2 \mathrm{~K}$
(d) $4 K^{*}$

Objective NCERT at your FINGERTIPS: Physics

NCERT 11th Edition

Chapter 7, Problem 82

Instant Answer

Solved by Expert Dheeraj Sharma

09/28/2021

Step 1

The initial kinetic energy of the system is given as $K = \frac{1}{2} I \omega^2$. Show more…

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A child is standing with folded hands at the centre of a plattorm rotating about its central axis, The kinetic energy of the system is $K$. Now, the child stretches his arms so that moment of inertia of the system doubled. Now, the kinetic energy of the system is (a) $\frac{K^{*}}{4}$ (b) $\frac{K}{2}$ (c) $2 \mathrm{~K}$ (d) $4 K^{*}$

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Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is the energy possessed by a rotating object, calculated as one-half times the moment of inertia multiplied by the square of the angular velocity. It helps quantify the energy due to the object’s rotational motion.

Moment of Inertia

The moment of inertia measures an object's resistance to changes in its rotation rate and depends on how the mass is distributed relative to the axis of rotation. Changes in body configuration affect the moment of inertia, which in turn impacts angular velocity and kinetic energy.

Angular Momentum Conservation

Angular momentum is defined as the product of the moment of inertia and the angular velocity. In the absence of external torques, angular momentum is conserved. This conservation law underpins the relationship between changes in moment of inertia and the resulting changes in angular velocity and kinetic energy in rotating systems.

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