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CBSE Class 11-science Answered

if the momentum of body decreases by 30% its kinetic energy decreased by
question image
Asked by bhargavchary19 | 23 Dec, 2022, 07:33: AM
answered-by-expert Expert Answer
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 left parenthesis space m space v space right parenthesis squared over m end style = begin mathsize 14px style fraction numerator p squared over denominator 2 m end fraction end style
Kinetic energy E = begin mathsize 14px style fraction numerator p squared over denominator 2 m end fraction end style   ........................(1)
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 ..............................(2)
 
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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