- #1
vinter
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I was reading the Principle of Equivalence which says that inertial mass is equal to the gravitational mass, though I am not very clear that why it should be written as a theorem. Here is what I read and the subsequent confusions that formed :-
First, to define the inertial mass, you fix a unit system. If you fix the SI system, you bring the object kept at the International Beauro of Weights and Measurements which is labeled 1 kg, apply a certain force on it and measure the acceleration; let it be a m/s^2. Now you bring another arbitrary object, label it m kg., apply the same force on it and measure its acceleration; let it be b m/s^2. Give a value to m such that m*b = 1 * a. This defines the inertial mass of the arbitrary object precisely.
Now, you assume that the gravitational force acting between two objects is directly proportional to the product of their inertial masses as defined above and inversely proportional to the square of the distance between them. Then you perform several experiments to find the constant of proprotionality. The constant you find this way will obviously be adjusted in a way that the masses you use in the gravitational force law formula are exactly equal to the inertial masses. And then, you suddenly become inquisitive and ask an important question - Are the masses coming in the gravitational force law equation equal to the inertial mass? To answer this, you again perform several experiments and find that they are, in fact, equal. You become excited and say that this is the beauty of the nature, state this thing as the "principle of equivalence" and subsequently conclude that God must be present (this last part was sarcasm). What the heck?
First, to define the inertial mass, you fix a unit system. If you fix the SI system, you bring the object kept at the International Beauro of Weights and Measurements which is labeled 1 kg, apply a certain force on it and measure the acceleration; let it be a m/s^2. Now you bring another arbitrary object, label it m kg., apply the same force on it and measure its acceleration; let it be b m/s^2. Give a value to m such that m*b = 1 * a. This defines the inertial mass of the arbitrary object precisely.
Now, you assume that the gravitational force acting between two objects is directly proportional to the product of their inertial masses as defined above and inversely proportional to the square of the distance between them. Then you perform several experiments to find the constant of proprotionality. The constant you find this way will obviously be adjusted in a way that the masses you use in the gravitational force law formula are exactly equal to the inertial masses. And then, you suddenly become inquisitive and ask an important question - Are the masses coming in the gravitational force law equation equal to the inertial mass? To answer this, you again perform several experiments and find that they are, in fact, equal. You become excited and say that this is the beauty of the nature, state this thing as the "principle of equivalence" and subsequently conclude that God must be present (this last part was sarcasm). What the heck?