If momentum of a body is measured with an error of +100%, the percentage error in the measuremnt of kinetic energy is?

Asked by anandcshaji | 16th Aug, 2014, 03:28: PM

Expert Answer:

W e space k n o w space t h a t comma space E space equals space fraction numerator P squared over denominator 2 m end fraction 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 %. 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. T h u s comma space i f space 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 % comma space t h e n space t h e space e r r o r space i n space c o r r e s p o n d i n g space K. E. space i s 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 space space space

Answered by Sheetal Jalan | 17th Aug, 2014, 12:35: PM