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Universal Law of Gravitation – Word Problem

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What is the Universal Law of Gravitation?

The universal law of gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

If there are two objects, A and B with masses 𝒎𝟏 and 𝒎𝟐, separated by a distance 𝒅, then the gravitational force between them is given by the following formula: 𝑭 = 𝑮/(𝒎𝟏 × 𝒎𝟐)/𝒅𝟐

Here, G is the universal gravitational constant.

Gravitational Force Formula

Universal Law of Gravitation: Word Problem

The mass of Zen is 70kg and that of Zara is 50kg. If the distance between them is 1 km, then calculate the force exerted by Zara on Zen.

Let 𝒎𝟏 be Zen’s mass, which is 70 kilograms, and 𝒎𝟐 be Zara’s mass, which is 50 kilograms. The distance d between them is 1 kilometer. Now, we need to convert the distance given in kilometers to meters. The distance d will equal 1000 meters. (𝑮 = 𝟔. 𝟕 × 𝟏𝟎−𝟏𝟏𝑵 𝒎𝟐 𝒌𝒈−𝟐)

Substituting the values in the formula:

𝑭 = (𝟔. 𝟕 × 𝟏𝟎−𝟏𝟏)𝑵 𝒎𝟐 𝒌𝒈−𝟐 × 𝟕𝟎𝒌𝒈 × 𝟓𝟎𝒌𝒈/𝟏𝟎𝟎𝟎𝒎𝟐

We get the value of F as 𝟐. 𝟑𝟒𝟓 × 𝟏𝟎−𝟏𝟑𝑵.

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