Force of Attraction Formula

Force of attraction is defined as a force that causes two or more objects to come together, even if they are not near to or touching one other. It is a force that attracts the bodies closer together. According to Newton’s universal law of gravity, every mass that exists in the cosmos attracts another mass, and everything which is thrown upwards is bound to fall back on the ground. Magnetic force, electric force, electrostatic force, and gravitational force are some attraction forces.

Force Of Attraction Formula

The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the distance between them. It is denoted by the symbol F_g. Its unit of measurement is Newton (N), and the dimensional formula is given by [M¹L¹T^-2]. Its formula is equal to the product of the gravitational constant and the ratio of the product of masses of the bodies to the square of the distance between them.

F_g = Gm₁m₂/r²

Where,

• F_g is the force of attraction,
• G is the gravitational constant with the value of 6.67 ×10⁻¹¹ Nm²/kg²,
• m₁ is the mass of a body,
• m₂ is the mass of other body,
• r is the distance between the two bodies.

Derivation

Consider a system of two bodies of masses m₁ and m₂ such that they are separated by a distance r. It is known that the force of attraction between these two bodies is directly proportional to the product of the masses of the bodies.

F ∝  m₁m₂ ⇢ (1)

Also, the force is indirectly proportional to the square of the distance between the two bodies. So we get,

F ∝  1/r² ⇢ (2)

From (1) and (2), 

F ∝  m₁m₂/r²

Replacing the proportionality sign with a constant, we get,

F_g = Gm₁m₂/r²

Here, G is known as the gravitational constant.

This derives the formula for force of attraction between two bodies.

Sample Problems

Problem 1: Calculate the gravitational force between two bodies of masses 50 kg and 100 kg separated by a distance of 20 m.

Solution:

m₁ = 50

m₂ = 100

r = 20

Using the formula we get,

F = Gm₁m₂/r²

= (6.67 ×10⁻¹¹ × 50 × 100)/(20)²

= 8.343 × 10^-10 N

Problem 2: Calculate the gravitational force between two bodies of masses 100 kg and 150 kg separated by a distance of 80 m.

Solution:

m₁ = 100

m₂ = 150

r = 80

Using the formula we get,

F = Gm₁m₂/r²

= (6.67 ×10⁻¹¹ × 100 × 150)/(80)²

= 1.5643 × 10^-10 N

Problem 3: Calculate the gravitational force between two bodies of masses 200 kg and 170 kg separated by a distance of 1000 m.

Solution:

m₁ = 200

m₂ = 170

r = 1000

Using the formula we get,

F = Gm₁m₂/r²

= (6.67 ×10⁻¹¹ × 200 × 170)/(1000)²

= 2.26 × 10^-12 N

Problem 4: Calculate the mass of the bodies if the gravitational force between them is 2.8 × 10^-12 N such that they have equal masses and are separated by a distance of 120 m.

Solution:

F = 2.8 × 10^-12

r = 120

Using the formula we get,

F = Gm²/r²

=> m² = Fr²/G

=> m² = (2.8 × 10^-12 × 120 × 120)/(6.67 ×10⁻¹¹)

=> m² = 625

=> m = 25 kg

Problem 5: Calculate the mass of the bodies if the gravitational force between them is 1.89 × 10^-11 N such that they have equal masses and are separated by a distance of 60 m.

Solution:

F = 1.89 × 10^-11

r = 60

Using the formula we get,

F = Gm²/r²

=> m² = Fr²/G

=> m² = (1.89 × 10^-11 × 60 × 60)/(6.67 ×10⁻¹¹)

=> m² = 1024

=> m = 32 kg

Problem 6: Calculate the distance between the bodies of masses 16 kg and 32 kg if the gravitational force between them is 4.2 × 10^-12 N.

Solution:

F = 4.2 × 10^-12

m₁ = 16

m₂ = 32

Using the formula we get,

F = Gm₁m₂/r²

=> r² = Gm₁m₂/F

=> r² = (6.67 ×10⁻¹¹ × 16 × 32)/(4.2 × 10^-12)

=> r² = 8100

=> r = 90 m

Problem 7: Calculate the distance between the bodies of masses 40 kg and 34 kg if the gravitational force between them is 2.6 × 10^-11 N.

Solution:

We have,

F = 2.6 × 10^-11

m₁ = 40

m₂ = 34

Using the formula we get,

F = Gm₁m₂/r²

=> r² = Gm₁m₂/F

=> r² = (6.67 ×10⁻¹¹ × 40 × 34)/(2.6 × 10^-11)

=> r² = 3600

=> r = 60 m