If the percentage error of momentum of a body is 100%, find the percentage error of the Kinetic energy of the body ising mass and velocity. 

Asked by akashsahaemailid | 17th Apr, 2020, 09:32: AM

Expert Answer:

W e space k n o w space t h a t comma space
E space equals space 1 half m v squared
rightwards double arrow E space equals space fraction numerator P squared over denominator 2 m end fraction space.... space left parenthesis m o m e n t u m comma space P space equals space m v right parenthesis
T h e space e r r o r space i n space m e a s u r e m e n t space o f space m o m e n t u m space i s space 100 percent sign.
T h e r e f o r e comma space t h e space a c t u a l space m o m e n t u m space w i t h space e r r o r comma space P apostrophe space equals space P space plus space P space equals space 2 P
T h e r e f o r e comma space K. E. space w i t h space e r r o r comma space E apostrophe space equals space fraction numerator left parenthesis P apostrophe right parenthesis squared over denominator 2 m end fraction equals space fraction numerator open parentheses 2 P close parentheses squared over denominator 2 m end fraction
o r comma space E apostrophe space equals space fraction numerator 4 P squared over denominator 2 m end fraction
o r comma space E apostrophe space equals space fraction numerator P squared over denominator 2 m end fraction space plus space 3 space open parentheses fraction numerator P squared over denominator 2 m end fraction close parentheses
o r comma space E apostrophe equals space E space plus space 3 space E space equals space 4 E
T h u s comma space t h e space K. E. space i n c r e a s e s space t h r e e space t i m e s.
S o comma space p e r c e n t a g e space c h a n g e space i n space K. E. space equals space fraction numerator F i n a l space K. E. space minus space I n i t i a l space K. E. over denominator I n i t i a l space K. E. space end fraction cross times 100
o r comma space space p e r c e n t a g e space c h a n g e space i n space K. E. space equals fraction numerator 4 E space minus space E over denominator E end fraction cross times 100 space equals space 300. space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 
 
Thus, if the percentage error in the momentum is 100% then the percentage error of kinetic energy is 300%

Answered by Shiwani Sawant | 17th Apr, 2020, 11:43: AM