Two solid spheres of radius R made of the same type of steel are placed in contact. The magnitude of the gravitational force the

Question

3 years ago

8

Two solid spheres of radius R made of the same type of steel are placed in contact. The magnitude of the gravitational force the

y exert on each other is F1. When two other solid spheres of radius 3R made of this steel are placed in contact, what is the magnitude of the grav force that they exert on each other?
A) F1
B) 3F1
C) 9F1
D) 81F1

Physics

1 answer:

dimulka [17.4K] · Answer 1 · 2022-06-01T04:59:15+03:00

F1 = G * m*m / [2r] ^2 = G * m^2 / 4r^2

Given the the mass is proportional to the volume and the volume is proportional to r^3, the mass of each big sphere is 3^3 = 27 times the mass of the small spheres. And the distance between the centers is 3r + 3r = 6r

F2 = G * [27m * 27m]/* [6r]^2 = G* 27^2 m^2 / 36r^2 = 81 G*m^2 / 4r^2 = 81*F1

Therefore, F2 = 81F1

Answer: option D) 81F1.