Question

If the error in the measurement of momentum of a particle is 50% ,then the error in the measurement of kinetic energy is how much?

a)75% b)125%

Answer 1

Momentum = mv = x (say)
Error in momentum = 50%
therefore momentum is taken as= 3x/2

Now KE = 1/2 mv^2 = 1/2 (m^2v^2/m) = 1/2 (mv)^2/m
KE =1/2 (3x/2)^2/m = 1/2 9x^2/4m=1/2 *9(mv)^2/4m =9/4* (1/2 mv^2)

Here it is clear 9/4 time of actual KE
Error = (9/4 -1) = 5/4

% of error =5/4 * 100 = 125% Ans