A uniform, solid, \(1000.0-\mathrm{kg}\) sphere has a radius of \(5.00 \mathrm{~m}\). (a) Find the gravitational force this sphere exerts on a \(2.00-\mathrm{kg}\) point mass placed at the following distances from the center of the sphere: (i) \(5.01 \mathrm{~m}\), (ii) \(2.50 \mathrm{~m}\). (b) Sketch a qualitative graph of the magnitude of the gravitational force this sphere exerts on a point mass \(m\) as a function of the distance \(r\) of \(m\) from the center of the sphere. Include the region from \(r=0\) to \(r \rightarrow \infty\).

Step 1 of 3

Introduction :

In this question, we need to force on the point mass at (i) \(5.01 \mathrm{~m}\) (ii) \(4.99 \mathrm{~m}\) (iii) \(2.72 \mathrm{~m}\)

In part (b) we need to plot graph of magnitude of gravitational force of sphere exerted on point mass as function of distance from \(\mathrm{r}=0\) to \(\mathrm{r}=\infty\)

Data given

Mass of spherical shell \(M=1000 \mathrm{~kg}\)

Mass of point mass \(m=2.0 \mathrm{~kg}\)

Radius of shell \(R=5.0 \mathrm{~m}\)

Distances

\(d_{1}=5.01 \mathrm{~m}\)

\(d_{2}=2.50 \mathrm{~m}\)