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dinesh2002k
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why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
The sum of masses would be inconsistent with the data. In particular, the acceleration would depend on the mass of both objects.dinesh2002k said:why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
The ultimate, but perhaps unsatisfactory answer, is that gravitational force depends on the product of the masses because that's just the way the universe works. One consequence of this is that if you change the mass of one of the two objects, the force changes proportionally. That is, if you double the mass of one object, the force also doubles. This would NOT be the case if the force was proportional to the sum of the masses.dinesh2002k said:why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
Sir can i know what this M mean (mass + something)Ibix said:So the force is proportional to the mass, and not to the mass plus something, right?
Let's consider that gravitational force is proportional to ##m+M##. Our gravitational force law near Earth's surface would be ##F=k(m+M)## where ##k## is a constant we don't know. What would the acceleration due to gravity be under this law? Is it independent of ##m##?
Thank you sir.Drakkith said:The ultimate, but perhaps unsatisfactory answer, is that gravitational force depends on the product of the masses because that's just the way the universe works. One consequence of this is that if you change the mass of one of the two objects, the force changes proportionally. That is, if you double the mass of one object, the force also doubles. This would NOT be the case if the force was proportional to the sum of the masses.
This would mean that, in cases where one object vastly out masses the other, such as stars vs planets, doubling the mass of the planet would add only negligible force while doubling the inertia. Two planets (or other objects much less massive than the star) of nonequal mass placed at the same distances from the star might experience wildly different orbits since their accelerations would be different. One might spiral outwards to infinity, or spiral inwards until it impacts the star.
Have you tried adding 1kg and 2kg to the mass of the Earth? Is the ratio of those sums consistent with the ratio of weight forces we measure for 1kg and 2kg test masses?dinesh2002k said:why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
The gravitational force (or rather interaction) is a fundamental notion in contemporary physics, i.e., the mathematical laws describing it correctly cannot be derived from any other more fundamental laws.dinesh2002k said:Sir , how do you say that the sum of masses would be inconsistent .I also request you to justify what makes multiplication of the masses correct.
We see experimentally that if you double either mass you double the force. The product of the masses does that. The sum of the masses does not.dinesh2002k said:why is that the gravitational force proportional to product of masses why not sum of masses or something else .........
Mass of earth being 5.97 × 10^24 kg , an added mass of 1kg or 2kg doesn't make a big difference in the gravitational forces ,I think , Sir.A.T. said:Have you tried adding 1kg and 2kg to the mass of the Earth? Is the ratio of those sums consistent with the ratio of weight forces we measure for 1kg and 2kg test masses?
Thank you sirDale said:We see experimentally that if you double either mass you double the force. The product of the masses does that. The sum of the masses does not.
Exactly. But we observe that the force on 2kg is twice the force on 1kg, which is consistent with a product, not a sum of the masses.dinesh2002k said:Mass of earth being 5.97 × 10^24 kg , an added mass of 1kg or 2kg doesn't make a big difference in the gravitational forces ,I think , Sir.
Understood.Thank you for response and guidance, Sir.A.T. said:Exactly. But we observe that the force on 2kg is twice the force on 1kg, which is consistent with a product, not a sum of the masses.
The law of universal gravitation states that the force of attraction between two objects is directly proportional to the product of their masses. This means that as the mass of one object increases, the gravitational force between the two objects also increases. This is because objects with larger masses have a greater gravitational pull.
The greater the mass of an object, the greater its gravitational force. This is because mass is directly proportional to gravitational force. Therefore, objects with larger masses have a stronger gravitational pull than objects with smaller masses.
The relationship between mass and gravitational force is directly proportional. This means that as one increases, the other also increases. This relationship is described by the equation F = G * (m1 * m2)/r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
If gravitational force was not proportional to mass product, then objects with different masses would experience different amounts of gravitational force, making it difficult to accurately predict their motion. By being directly proportional to mass product, the law of universal gravitation allows us to understand and predict the behavior of objects in the presence of gravity.
The law of universal gravitation also states that the force of attraction between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases. This is why objects on Earth experience less gravitational force from the Sun compared to objects on Mercury, which is closer to the Sun.