Question

Suppose we tried to do this problem for the ball of radius 1 centered at the point (0,1,0). Why is this problem harder with the new ball?

a) Increased gravitational force
b) Change in surface area
c) Altered center of mass
d) Different velocity vector

Answer 1

The problem is more difficult because the ball's altered center of mass can affect its gravitational interactions and resultant motion. The force required is dependent on both the mass distribution and force application point, not just the radius.

Step-by-step explanation:

The problem of determining the gravitational force on a ball of radius 1 centered at the point (0,1,0) would likely be more difficult because of an altered center of mass if the ball is not homogeneous in density. Considering the gravitational force, it is neither directly proportional nor inversely proportional to the radius of the circular orbit as it depends on the mass distribution and distance from the attracting body. In a situation where two balls are thrown, they will not necessarily travel the same distance if the angle of throw differs. Additionally, the centripetal acceleration vector is always perpendicular to the velocity vector of a body in circular motion. Factors such as distribution of mass can affect how much force is needed to change the momentum or stop a rotating body, as seen in the example of a merry-go-round where force applied at different radii can impact the time taken to achieve a certain angular velocity or to stop the rotation.