NEET Class neet Answered
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
Asked by ayush.gupta3052 | 10 Jul, 2021, 19:01: PM
Let
i be initial moment of inertia of system and ωi be the initial angular speed of rotation .
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
Let
f be final moment of inertia of system and ωf be the final angular speed of rotation .
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
By Conservation of angular momentum , we have ,
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
Final moment of Inertia
f = 2
i ...................... (2)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
Hence , we get from eqn.(1) , ωf = (1/2)ωi
Final kinetic energy = (1/2)
f ωf2 = (1/2) ( 2
i ) [ (1/2)ωi ]2 = (1/4)
i ωi2
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
![begin mathsize 14px style straight I end style](https://images.topperlearning.com/topper/tinymce/cache/8cde8e660e1a71a3a580fc3a20f88fc1.png)
Hence Final kinetic energy becomes (1/4)th of initial kinetic energy
Answered by Thiyagarajan K | 10 Jul, 2021, 20:16: PM
NEET neet - Physics
Asked by 69sayyappan | 29 Mar, 2024, 10:44: AM
NEET neet - Physics
Asked by anandibastavade555 | 24 Mar, 2024, 13:03: PM
NEET neet - Physics
Asked by snowgaming267 | 21 Mar, 2024, 13:44: PM
NEET neet - Physics
Asked by vikrantdhurdev2020 | 15 Mar, 2024, 16:10: PM
NEET neet - Physics
Asked by vijayyadav08735 | 20 Feb, 2024, 15:18: PM
NEET neet - Physics
Asked by meheboob1doctor | 21 Dec, 2022, 09:09: AM