Final answer:
The centripetal acceleration of a child at the low point of a circular path is equal to g, the acceleration due to gravity, assuming no other forces like friction or tension are at play. The correct answer is option A) g.
Step-by-step explanation:
Understanding Centripetal Acceleration
When discussing the motion of objects in a circular path, centripetal acceleration is a crucial concept. The question asks for the centripetal acceleration of a child at the low point of a swing or circular motion. According to physics, at the bottom of the swing, the acceleration that keeps the child moving in a circular path (not accounting for any pendulum-like swinging motion) is directed towards the center of the circle, which is the centripetal acceleration.
Calculating Centripetal Acceleration
The centripetal acceleration (ac) can be calculated using the formula:
ac = v^2 / r
Where v is the velocity of the object and r is the radius of the circular path. At the low point, the child is experiencing the full force of gravity, which acts in the same direction as the centripetal force required to keep the child in circular motion. Therefore, at this point, the centripetal acceleration would be equal to g, the acceleration due to gravity, assuming no other forces are at play such as friction or tension in a pendulum.
Answer to the Question
The correct answer to the question of what is the centripetal acceleration of the child at the low point is option A) g (acceleration due to gravity).