A solid uniform sphere has a mass of 3.0 multiplied by 104 kg and a radius of 1.

Question

A solid uniform sphere has a mass of 3.0 multiplied by 104 kg and a radius of 1.4 m.

(a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of 2.2 m from the center of the sphere? (Use the following as necessary: m, where m is in kg.)
F = _____ N

(b) What if it is 1.0 m from the center of the sphere? (Use any variable or symbol stated above as necessary.)
F = _____ N

(c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r 1.4 m from the center of the sphere. (Use any variable or symbol stated above as necessary.)
F =_____ N

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Explanation / Answer

a) F = Gm1m2/ r2

G = 6.67 x 10-11 m3/kg sec2

M1 = 312 kg

M2 = M kg. , r = 3.6 m i.e,    ( 2.2m + 1.4m)

F = 6.67 x 10-11x 312 x M/ 3.62

F = 160.5x10-11*M Newtons

b) If it is 1 m from the centre of the sphere, then r = 1+1.4 = 2.4 m

F = 361.29 x 10-11 x M Newtons

c) General expression : ) F = Gm1m2/ 2.82 Newton

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