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 , one quarter circle, the center 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 center 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  , one quarter circle, the center 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 center of the circle.

Quizplus · Accepted Answer

When the two cars start, they are at the same point, so the center of mass is at the center of the circle. As they move in opposite directions, the center of mass remains fixed, since the two movements cancel each other out.

When each car has traveled a quarter of the circle, they are diametrically opposite each other. At this point, the center of mass is still fixed, since the two cars are equidistant from it.

When each car has traveled a distance less than a quarter of the circle, the center of mass is still fixed, since the two cars have not yet moved far enough to cause a significant shift.

However, once each car has traveled a distance greater than a quarter of the circle, the center of mass will shift towards the faster car. This is because the faster car covers a greater distance in the same amount of time, causing it to "catch up" with the slower car.

Since each car travels for a distance less than a quarter of the circle, the center of mass remains fixed at the center of the circle.

However, the question asks about the movement of the center of mass while each car travels a distance less than 11eb6adc_ed01_322b_b0cf_fbe08d79c216_TB8245_11, one quarter of the circle. At this distance, the two cars have not yet moved far enough to cause a significant shift in the center of mass.

Therefore, the center of mass remains fixed at the center of the circle, which is also a diameter. Since the two cars are moving in opposite directions along the circumference of the circle, the center of mass is moving along the diameter of the circle at a constant speed v', which is equal to 0.

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