Question

Two spheres of the same material, radius 2r, are in contact with each other. The gravitational attraction between them is given by:

(a) Gm²​/(4r)²
(b) 2Gm²/(4r)²​
(c) 4Gm²/(4r)²​
(d) 8Gm²/(4r)²

Answer 1

The gravitational attraction between the two sphere, given that ther are of the same material and radius of 2r, is
`(GM^2)/((4r)^2)` (option A)

How to calculate the gravitational attraction between the two spheres?

Gravitational attraction is given by the following formula:

`F = (GM_1M_2)/(r^2)`

Where

• F is the gravitational attraction
• M₁ and M₂ are masses of objects
• r is the distance apart

Now, we shall consider the question given in order to calculate the gravitational attraction between the two spheres. Details below:

• Mass of first sphere (M₁) = M
• Mass of second sphere (M₂) = Mass of first sphere (M₁) = M (same material)
• Radius of each sphere = 2r
• Distance apart (r) = 2 × 2r = 4r
• Gravitational constant (G) = G
• Gravitational attraction (F) =?

`F = (GM_1M_2)/(r^2)\\\\F = (G\ *\ M\ *\ M)/((4r)^2)\\\\F = (GM^2)/((4r)^2)`

In conclusion, the correct answer is option A