ALL TIME DOUBT SERVICE

had a problem in this all through class 11 so i memorized the result. This was the only result that i memorized in physics in 11 and LOL it proved fruitful!! But i hate the concept of memorizing so i hpe my doubt will be answered in this GENIUS forum...

the problem goes like this:

If the error in the measurement of the momentum of a particle be +100%. Then, the error in the measurement of kinetic energy is:
(a)400%
(b)300%
(c)100%
(d)200%

but before delving into this question let us solve this question...

%age error in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy will be??

well to solve this problem after using much mathmatical concepts we conclude that
if E=¹/₂mv²,
then, \frac{\Delta E}{E}=\frac{\Delta m}{m}+2\frac{\Delta v}{v}
or, %age error in E=2%+2X3%=8%........which is the correct answer...

now delving back into the original quest...

we know after applying much physics, we get,
p=√2mE
so, E=^p2/_4m²
or, \frac{\Delta E}{E}=2\frac{\Delta p}{p}

giving %age change in E=200%

but in all books i found answer given is 300%

even in our exams a question came asking for when the change in K.E. is 100% what is the change in linear momentum, I instead of applying the above technique, straightaway did ¹⁰⁰/₃% and when papers came out LOL the teacher had given 0.5 out of 1 with the comment "half marks for correct answer without any work out..i must mention others had acheved a 0".[3][3][3] So now that my 11 is over, i want the explanation for this so that i do not get any more HALF MARKS in life for these types of questions!![3][3][3]