Answer explanation:

Option 1 - 2: This is the correct answer. Kinetic energy (KE) and linear momentum (p) have a quadratic relationship, meaning, if you double the momentum, the kinetic energy will quadruple (since KE = p^2/2m, where m represents mass). However, in the question, it`s said that linear momentum changes by two times, which can be understood as p = 2p (original). So considering the expression, KE = (2p)^2/2m = 4p^2/2m = 2KE (Original), hence, the kinetic energy changes by a factor of 2.

Option 2 - 4: This is incorrect. Quadrupling the kinetic energy requires quadrupling the momentum, which is not mentioned in the question.

Option 3 - 6: This is also incorrect, an increase in kinetic energy by a factor of 6 would require the momentum to be multiplied by √6, not 2.

Option 4 - 8: This option is incorrect because it would require the momentum to be multiplied by √8, not 2.