Two uniform spherical shells are located such that their centers are along the x

Question

Two uniform spherical shells are located such that their centers are along the x axis in (Figure 1) . The inner shell has mass minner and radius R, and its center is atx = 0.80R. The outer shell has mass 3.0minner and radius 2.0R, and its center is at x = 0.

a.

What is the magnitude of the vector sum of the gravitational forces exerted by these two shells on an object of mass mobj placed at x = 3.0R.

Express your answer in terms of some or all of the variables minner, mobj, R, and gravitational constant G.

b. What is the magnitude of the vector sum of the gravitational forces exerted by these two shells on an object of mass mobj placed at x = 1.9R.

Express your answer in terms of some or all of the variables minner, mobj, R, and gravitational constant G.

c.

What is the magnitude of the vector sum of the gravitational forces exerted by these two shells on an object of mass mobj placed at x = 0.90R.

Express your answer in terms of some or all of the variables minner, mobj, R, and gravitational constant G.

Explanation / Answer

from Newtons aw of gravitation F = Gm1m2/r^2

where m1 and m2 are the masses

r is the distance

so

F = G m inner *mouter / (distance)2

m outer=3*m inner

distance=2R

F = 3G ( m inner / 2*R)2
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(b) m2 = 2 mobj

distance x = 1.9 R

so

F = 3G (m inner )2*m obj) / (1.9R)^2

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(c) F = 3G (m inner)2 * m obj / ( (0.80 R)^2+ (0.90 R)2 )^3/2

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