The formula relating kinetic energy and momentum of a particle is expressed as
KE = p^2/2m
let the actual momentum be p. Since the error measurement is 10%, the measurement of the momentum would be
p + 0.1p = 1.1p
Percentage error in the measurement of the kinetic energy is obtained by the formula,
% error = (KEf - KEi)/KEi x 100
where
KEf is the final kinetic energy measured error
KEi is the initial kinetic energy measured without error
Thus,
% error = [(1.1p)^2/2m - p^2/2m)]/p^2/2m x 100
% error = p^2/2m(1.1^2 - 1)/(p^2/2m) x 100
% error = 100(1.1^2 - 1)
% error = 21%