Imagine two pairs of books. In the first pair, two books of mass m_1m 1 ​ m, start subscript, 1, end subscript and m_2m 2 ​ m, start subscript, 2, end subscript are separated by the distance rrr, resulting in a gravitational force F_1F 1 ​ F, start subscript, 1, end subscript. In the second pair, two books of mass 2m_12m 1 ​ 2, m, start subscript, 1, end subscript and 4m_24m 2 ​ 4, m, start subscript, 2, end subscript are separated by the distance 2r2r2, r, resulting in a gravitational force of F_2F 2 ​ F, start subscript, 2, end subscript. The relationship between these two forces can be written as F_2 = nF_1F 2 ​ =nF 1 ​ F, start subscript, 2, end subscript, equals, n, F, start subscript, 1, end subscript. In the expression F_2 = nF_1F 2 ​ =nF 1 ​ F, start subscript, 2, end subscript, equals, n, F, start subscript, 1, end subscript, what is the value of nnn?

The value of n in the relationship between F₁ and F₂, (F₂ = n·F₁), is n = 2

The reason for the above value is as follows;

The given parameters of the first pair of books are;

The masses of the books = m₁, and m₂

The distance between the two m₁ and m₂ = r

The gravitational force between the masses = F₁

The given parameters of the second pair of books are;

The masses of the books second pair = 2·m₁, and 4·m₂

The distance between the two masses in second pair = 2·r

The gravitational force between the masses in second pair = F₂

The relationship between the two forces is F₂ = n·F₁

The required parameter;

The value of n in F₂ = n·F₁

According to Newton's law of universal gravitation, we have;

Therefore, we get;

Therefore;

F₂ = 2·F₁

The value of n in F₂ = n·F₁ is n = 2

Learn more about gravitational force between masses here;

atomic = no of protons.

mass number-atomic number = neutron number

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