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If /11 is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle's belief was logically inconsistent by the following argument. Tie III and M together to form a double stone. Then, in falling, III should retard M, because it tends to fall more slowly, and the combination would fall faster than III but more slowly than M; but according to Aristotle the double body (M + /11) is heavier than M and, hence, should fall faster than M. If you accept Galileo's reasoning as correct, can you conclude that M and III must fall at the same rate? What need is there for experiment in that case? If you believe Galileo's reasoning is incorrect, explain why.

If /11 is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle's belief was logically inconsistent by the following argument. Tie III and M together to form a double stone. Then, in falling, III should retard M, because it tends to fall more slowly, and the combination would fall faster than III but more slowly than M; but according to Aristotle the double body (M + /11) is heavier than M and, hence, should fall faster than M. If you accept Galileo's reasoning as correct, can you conclude that M and III must fall at the same rate? What need is there for experiment in that case? If you believe Galileo's reasoning is incorrect, explain why.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
First we consider the Galileo argument on the motion of the falling object. He asserted that if two stones one of mass m smaller than mass M are tied together, the smaller acceleration felt by the smaller mass must retard the motion of the higher mass such that the net acceleration of the system lies between the acceleration of the smaller mass and the acceleration of the larger mass thereby contradicting the Aristotle argument. Galileo questioned that how a larger mass stone felt at a slower rate relative to the one allowed by nature, under free fall, due to the retard from the smaller mass.
Aristotle counterargument that the tied system has a combined mass more that the mass of the massive stone highlighting that both the stones with masses m and M will fall at a rate more than allowed for the higher mass stone. Therefore the system will fall more quickly relative to the fall rate of the higher mass stone.
One must question that is it possible for a stone to increase the mass of the other stone while falling an account for the knowledge that they are connected. How it is that without any tension in the string through which they are tied, the system could combine its mass and move faster as stated by Aristotle. Only when the higher mass stone goes faster than the lower mass stone, the system can move together.
Therefore till the time there is no tension in the string, the motion of the objects must support the Galileo view. When the experiment was performed in a closed room, so as to minimize the effect of the air resistance, there was no lag or lead observed between the motions of the stone thereby proving that both have fallen at the same rate.
Galileo himself solved the problem of air resistance by performing the experiment on the inclined plane. This also helped him to reduce the rate of fall of the objects and allowed to make accurate measurements.

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