Question

Two skyscrapers are located next to each other. one has a mass of kg, and the other has a mass of kg. their respective centers of mass are a distance of m apart. what is the force of the gravitational attraction between the two buildings

Answer 1

The gravitational force of attraction between the two skyscrapers is approximately 617 Newtons, (A).

How to find force?

To calculate the gravitational force of attraction between the two skyscrapers, Newton's law of universal gravitation:

`\[ F = G (m_1 m_2)/(r^2) \]`

where:

F = gravitational force,

G = gravitational constant (
`\( 6.674 * 10^(-11) \, \text{Nm}^2/\text{kg}^2 \)`),

m₁ and m₂ = masses of the skyscrapers (2.04 × 10⁸ kg and 1.77 × 10⁸ kg respectively),

r = distance between their centers of mass (62.5 m).

Plugging in the values:

`\[ F = 6.674 * 10^(-11) ((2.04 * 10^8) * (1.77 * 10^8))/((62.5)^2) \]`

`\[ F = 6.674 * 10^(-11) * (3.6108 * 10^(16))/(3906.25) \]`

`\[ F = 6.674 * 10^(-11) * 9.2404448 * 10^(12) \]`

F ≈ 616.92106752 N

Rounded to the nearest whole number, the force is approximately 617 N.

Complete question:

Two skyscrapers are located next to each other. One has a mass of 2.04*10^8 kg, and the other has a mass of 1.77*10^8 kg. Their respective centers of mass are a distance of 62.5 m apart. What is the force of the gravitational attraction between the two buildings? Choose one answer.

a) 617 N

b) 38,600 N

c) 2490 N

d) 7710 N