CBSE Class 11-science Answered
if the momentum of body decreases by 30% its kinetic energy decreased by
![question image](http://images.topperlearning.com/topper/new-ate/top_mob16717610311688216442Screenshot_20221223-072723_OneDrive.jpg)
Asked by bhargavchary19 | 23 Dec, 2022, 07:33: AM
Momentum p = ( m v )
where m is mass and v is velocity
Kinetic energy E = (1/2) m v2 = (1/2)
= ![begin mathsize 14px style fraction numerator p squared over denominator 2 m end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/2bed43cb1ab0f4f1782b5dbb9c2d2c55.png)
![begin mathsize 14px style left parenthesis space m space v space right parenthesis squared over m end style](https://images.topperlearning.com/topper/tinymce/cache/c53f3733a654489913f0851ca08b2878.png)
![begin mathsize 14px style fraction numerator p squared over denominator 2 m end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/2bed43cb1ab0f4f1782b5dbb9c2d2c55.png)
Kinetic energy E =
........................(1)
![begin mathsize 14px style fraction numerator p squared over denominator 2 m end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/2bed43cb1ab0f4f1782b5dbb9c2d2c55.png)
if we differentiate above expression, we get
![begin mathsize 14px style increment E space equals open parentheses fraction numerator 2 space p over denominator 2 m end fraction close parentheses space increment p end style](https://images.topperlearning.com/topper/tinymce/cache/363c02ab5fc31d79fdd45c02ddb16db1.png)
where change in kinetic energy is given as ΔE and change in momentum is given as Δp
By dividing eqn.(2) by eqn.(1)
(ΔE/E) = 2 ( Δp / p )
Hence if momentum decreases by 30% , kinetic energy decreases by 60%
Answered by Thiyagarajan K | 23 Dec, 2022, 09:02: AM
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