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A solid sphere of uniform density has a mass of 6.1 × 104 kg and a...

A solid sphere of uniform density has a mass of 6.1 × 104 kg and a radius of 2.7 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 2.0 kg located at a distance of (a) 5.9 m and (b) 2.1 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r ? 2.7 m from the center of the sphere.

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Answer #1

given mass of the solid sphere M = 6.1 X 104 kg

adius of = 2.7 m = R

m = a particle of mass 2.0 kg

G = 6.67 X 10-11 N-m2/Kg2

a )

x = 5.9 m

using

F = G M m / x2

= 6.67 X 10-11 X 6.1 X 104 X 2 / 5.92

F = 2.3376 X 10-7 N

b )

x = 2.1 m

M' = M ( x/R )3  

F = G M ' m / x2

= G M m x / R3

= 6.67 X 10-11 X 6.1 X 104 X 2 X 2.1 / 2.73

F = 8.6818 X 10-7 N

c )

= 6.1 X 104 / ( 4 X 3.14 X 2.73 / 3 )

= 740.235 m3

F = G M ' m / r2

= G ( 4 X 3.14 X r3 X m / 3 r2 )

= G ( 4 X 3.14 X r X X m / 3)

= 6.67 X 10-11 X 4 X 3.14 X r X 740.235 X m / 3

F = 2.0671 X 10-7 m r N

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