Two particles of massesm1 andm2 are placed at a distancer. The ratio of gravitational force on massm1 due tomassm2 and on massm2 due to massm1
Question
Two particles of massesm1 andm2 are placed at a distancer. The ratio of gravitational force on massm1 due tomassm2 and on massm2 due to massm1
Solution
The gravitational force between two objects is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
- F is the force between the masses,
- G is the gravitational constant,
- m1 and m2 are the two masses, and
- r is the distance between the centers of the two masses.
The force on m1 due to m2 is F12 = G * (m1 * m2) / r^2 The force on m2 due to m1 is F21 = G * (m1 * m2) / r^2
As you can see, the forces are the same. The gravitational force that mass m1 exerts on mass m2 is the same as the force that mass m2 exerts on mass m1. This is a consequence of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Therefore, the ratio of the gravitational force on m1 due to m2 to the gravitational force on m2 due to m1 is 1:1.
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