Q.Two identical water bottles, one empty and the other filled with water, are allowed to roll down an inclined plane. Which one of them reaches the bottom first? Explain your answer.

For a round object of mass $m$ and radius $R$ rolling without slipping down an incline of angle $\theta$, two forces act along the slope: the driving component of gravity, $mg\sin\theta$, and an opposing static frictional force $f$ (the perpendicular component $mg\cos\theta$ is simply balanced by the normal force $N$). …