Question

Two 10kg spheres are placed 500mm apart.Express the gravitational attraction acting on one of the spheres as percentage of its weight on earth

Answer 1

Answer on Question #62334 - Physics – Astronomy, Astrophysics

Two 10kg spheres are placed 500mm apart. Express the gravitational attraction acting on one of the spheres as percentage of its weight on Earth.

Solution:

According to the law of universal gravitation, attraction force, acting on the sphere, is equal to

$$F _ {1 2} = G \frac {m _ {1} m _ {2}}{r ^ {2}},$$

where $G = 6.674 \times 10^{-11} N(m / kg)^2$ is the gravitational constant, $m_{1} = m_{2} = 10kg$ are masses of the spheres, $r = 500mm = 0.5m$ are the distance between them. On Earth weight of the sphere is

$$F _ {1} = m _ {1} g,$$

where $g = 9.81 \, N / kg$ is gravitational acceleration on Earth. Then

$$\frac {F _ {1 2}}{F _ {1}} = \frac {G m _ {1} m _ {2}}{r ^ {2} m _ {1} g} = \frac {G m _ {2}}{r ^ {2} g} = \frac {6 . 6 7 4 \times 1 0 ^ {- 1 1} \times 1 0}{0 . 2 5 \times 9 . 8 1} = 2. 7 3 1 \times 1 0 ^ {- 1 0} = 2. 7 3 1 \times 1 0 ^ {- 8} \%$$

Answer: attraction acting on the sphere is $2.731 \times 10^{-8}\%$ of its weight on Earth.

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