Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than $\frac{\pi}{2} \mathrm{R}$ , one quarter circle, the centre of mass of the two cars: A)remains at the initial point. B)travels along a diameter of the circle at speed v' v. E)remains at the centre of the circle.

Question

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than $\frac{\pi}{2} \mathrm{R}$ , one quarter circle, the centre of mass of the two cars:
A)remains at the initial point.
B)travels along a diameter of the circle at speed v' < v.
C)travels along a diameter of the circle at speed v' = v.
D)travels along a diameter of the circle at speed v' > v.
E)remains at the centre of the circle.

Quizplus · Accepted Answer

Since the two cars are moving in opposite directions, their velocities are in opposite directions too. Therefore, the vector sum of their velocities is zero at all times. Thus, the centre of mass of the two cars remains at the initial point. However, while each car travels a distance less than a quarter circle, their positions are such that the line joining them passes through the centre of the circle. Therefore, the centre of mass of the two cars travels along a diameter of the circle, but at a slower speed than either of the cars, and the answer is B.

Two Cars Start at the Same Point, but Travel in Opposite