The position vector of a particle is given by \vec{r} = \sqrt{3}t^2 \hat{i} + \sqrt{2}t \hat{j} + \sqrt{5} \hat{k}. Which one of the following statements is correct?

  1. A. The force acting on the particle is parallel to the instantaneous momentum of the particle.
  2. B. The force acting on the particle is perpendicular to the instantaneous momentum of the particle.
  3. C. The particle experiences zero force.
  4. D. The force acting on the particle is not parallel to the instantaneous momentum of the particle. ✓

Correct Answer: D. The force acting on the particle is not parallel to the instantaneous momentum of the particle.

Explanation

Velocity \vec{v} = 2\sqrt{3}t \hat{i} + \sqrt{2} \hat{j} and acceleration \vec{a} = 2\sqrt{3} \hat{i}. Force is proportional to \vec{a} (only in \hat{i} direction), while momentum is proportional to \vec{v} (has both \hat{i} and \hat{j} components). Thus, force and momentum are not parallel.

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