Final answer:
The gravitational force exerted by R on S is greater than the gravitational force exerted by S on R due to their different masses. Additionally, R will experience a smaller acceleration than S.
Step-by-step explanation:
The gravitational force exerted by an object on another object depends on the masses of the two objects and the distance between them. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
In this case, asteroid R is 10 times the mass of asteroid S. Therefore, the gravitational force exerted by R on S is greater than the gravitational force exerted by S on R. This is because the force is directly proportional to the masses, and R has a greater mass.
As for the acceleration, the gravitational force experienced by an object is directly proportional to its mass. Since R is more massive, it will experience a smaller acceleration than S.