Gravity and superpostion of two spheres

[J-dizzal]

Homework Statement

The figure shows a spherical hollow inside a lead sphere of radius R = 4.6 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 245 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 20 kg that lies at a distance d = 14 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?

Homework Equations

The Attempt at a Solution

when i find the mass of the "hollowed out" sphere its much larger than the larger sphere. I don't know how else to approach this problem.

 

[mfb]

The mass of the sphere is inconsistent with its given diameter and the density of lead. I would ignore the given "lead" and calculate the density based on the given size and mass.

 

[J-dizzal]

The mass of the sphere is inconsistent with its given diameter and the density of lead. I would ignore the given "lead" and calculate the density based on the given size and mass.

I updated my original photo with my calculations. Would the total force be the force of the full sphere minus the force of the "hollow" sphere? F=F₁-F₂? I got the wrong answer not sure where i went wrong.

 

[gneill]

Your volume and density calculations don't look right to me. Can you recheck them?

 

[J-dizzal]

Your volume and density calculations don't look right to me. Can you recheck them?

Thank you! I am having problem getting adjusted to an hp 300s+, I often have to double check its picking up all the buttons i press.

 

[mfb]

I updated my original photo with my calculations. Would the total force be the force of the full sphere minus the force of the "hollow" sphere? F=F₁-F₂?

Right (if you take both F1 and F2 to be positive).
A quick check: is your mass ratio 1 to 8?
The ratio of forces should be a bit smaller than that (1 to 7.something or 6.something) as the smaller sphere is a bit closer. If that is not true, something is wrong.