A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. The acceleration of the ball at the top of its path is:

a. at its maximum value for the ball's flight.

b. equal to the acceleration at the surface of the asteroid.

c. equal to one-half the acceleration at the surface of the asteroid.

d. equal to one-fourth the acceleration at the surface of the asteroid.

(d) equal to one-fourth the acceleration at the surface of the asteroid.

Explanation:

From Newton's gravitational law, force between two objects (planet) is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.

Case 1: when the ball rises to a height equal to the asteroid's radius

height, h = r

Case 2: when the ball rises to a height equal to the asteroid's radius and falls straight down toward the surface of the asteroid.

At top of its path, total height is 2r.

h = 2r

Therefore, the acceleration of the ball at the top of its path is equal to one-fourth the acceleration at the surface of the asteroid.

Option "d"

the first, second, and fifth options