Question

A uniform solid sphere of radius R produces a gravitational acceleration of ag on its surface. At what distance from the sphere’s center are there points (a) inside and (b) outside the sphere where the gravitational acceleration is ag/3?

Answer 1

To find the distance from the center of a uniform solid sphere where the gravitational acceleration is ag/3, we can use the inverse square law of gravity and solve equations for points inside and outside the sphere.

Step-by-step explanation:

To find the distance from the center of a uniform solid sphere where the gravitational acceleration is ag/3, we can use the inverse square law of gravity:

ag = GM/R^2

where G is the gravitational constant, M is the mass of the sphere, and R is the radius of the sphere. Rearranging the equation, we get:

R^2 = GM/ag

Let's call the distance from the center to the desired point as x. For a point inside the sphere, we have:

(ag/3) = G(M/(R-x)^2)

For a point outside the sphere, we have:

(ag/3) = G(M/(R+x)^2)

Solving these equations for x will give us the distance from the center for each case.