Question

A solid sphere of uniform density has a mass of 8.4 × 104 kg and a radius of 4.0 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 9.8 kg located at a distance of (a) 19 m and (b) 0.52 m from the center of the sphere

Answer 1

(a) GF = 1.522 x (10 ^ -7) N

(b) GF = 2.032 x (10 ^ -4) N

Step-by-step explanation:

The magnitude of the gravitational force follows this equation :

GF = (G x m1 x m2) / (d ^ 2)

Where G is the gravitational constant universal.

G = 6.674 x (10 ^ -11).{[N.(m^ 2)] / (Kg ^ 2)}

m1 is the mass from the first body

m2 is the mass from the second body

And d is the distance between each center of mass

m2 is a particle so m2 it is a center of mass itself

The center of mass from the sphere is in it center because the sphere has uniform density

For (a) d = 19 m

GF = {6.674 x (10 ^ -11).{[N.(m ^ 2)] / (Kg ^ 2)} x 8.4 x (10 ^ 4) Kg x 9.8 Kg} / [(19 m)^ 2]

GF = 1.522 x (10 ^ -7) N

For (b) d = 0.52 m

GF = 2.032 x (10 ^ -4) N

Notice that we have got all the data in congruent units

Also notice that the force in (b) is bigger than the force in (a) because the distance is shorter

Answer 2

a)
`F_a=0.152 \mu N`

b)
`F_b=203.182 \mu N`

Step-by-step explanation:

The center of mass of an homogeneous sphere is its center, therefore you can use Newton's universal law of gravitation to find both questions.

`F_g=G(m_1m_2)/(d)`

`G=6.674*10^(-11) NmKg^(-2)`

a) d = 19m

`F_a = G(8.4*10^(4)*9.8)/(19^2)`

`F_a=0.152 \mu N`

b) d = 0.52

`F_b = G(8.4*10^(4)*9.8)/(0.52^2)`

`F_b=203.182 \mu N`