two masses 1kg n 10kg r dropped from the same height above the ground .state with reason which mass will hit the ground earlier
Answers
Answer:
If a 10kg stone and a 1kg stone is dropped from the same height which will reach the ground first?
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The answer to this question was given by Galileo Galilei in one of his experiments of dropping objects from the leaning tower of Pisa. So what he did was, he dropped two spheres having different masses from top of the tower and calculated the time of descent for both the spheres. It was observed that both spheres took equal time to reach the ground irrespective of their masses. The outcome of this experiment was contrary to Aristotle's claim that heavier bodies fall faster than lighter ones.
Also, following his experiments Galileo formulated the equation for a falling body: d=1/2 g(t^2), where d was the height from which the objects was dropped, t was the total time which it took to cover that height d and g was the gravitational acceleration.
So how did this happen ?
Here we shall assume that the resistance by air is negligible and both the bodies are dropped ie, they have zero initial speed and thus both the spheres are performing free fall. That is no external force is acting on these spheres except for the force of gravity. This force of gravity is what causes both the spheres to accelerate downwards.The force of gravity experienced by an object is dependent upon the mass of that object. That is the heavier mass will experience more gravitational pull than the lighter one or the Earth is pulling downwards upon the heavier sphere with more force than it pulls downwards upon the lighter one. So why is it observed that both of them took same time to reach the ground ?
To understand this let us recall Newton’s second law of motion which states that net force acting on a body is equal to the product of mass and its acceleration {F=Ma} .
Hence, the acceleration is the ratio of force to mass { a= F/M }.
We know that only force acting here is the weight of the sphere , F=Mg (weight of the sphere), g is the gravitational acceleration {9.8 m/s^2 on Earth} . Therefore a=F/M, a=Mg/M , hence a=g.
Same will be the case of second sphere and we can see that both the objects are falling under the influence of constant acceleration whose value is g.
Using the Galileo’s relation d=1/2 g (t^2) we can see that both the spheres have same acceleration g, cover same height d so their time periods have to be same.