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

Answer:

a) $F_a=0.152 \mu N$

b) $F_b=203.182 \mu N$

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.

$F_g=G\frac{m_1m_2}{d}$

$G=6.674*10^{-11} NmKg^{-2}$

a) d = 19m

$F_a = G\frac{8.4*10^{4}*9.8}{19^2}$

$F_a=0.152 \mu N$

b) d = 0.52

$F_b = G\frac{8.4*10^{4}*9.8}{0.52^2}$

$F_b=203.182 \mu N$

Answer 2

Answer:

(a) GF = 1.522 x (10 ^ -7)  N

(b) GF = 2.032 x (10 ^ -4)  N

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