Question

two body of different masses fall from different height what is the ratio of time taken​

Answer 1

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Answer 2

Answer:

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The heavier object will reach the ground first.

Yes, Galileo and subsequent physics shows that mass is not a factor for acceleration in a gravitational field, so the schoolboy answer is that they reach the ground at the same time.

But that disregards air resistance, which the question states “is the same” for the two objects. So that implies there is some.

Air resistance is properly called drag, and is expressed by the equation:

Fd=Cd12ρAV2

This states that the drag force is equal to the drag coefficient times half the air (or other fluid) density times the frontal area times the velocity squared. Drag coefficient is just a number that depends on the object’s shape. A sphere has a Cd of about 0.5, but a streamlined bullet-shaped object might have a Cd of 0.1 No mention of mass here, but we also know from Newton’s Second Law that

F=ma

So for a falling body, where a is the acceleration due to gravity and the mass is the object’s mass, that at some velocity, Fd will equal the object’s weight. At this velocity, the mass will stop accelerating and maintain a constant velocity. This is called the terminal velocity, and does depend on mass. If we set Fd=mg , we can solve for V, and find the terminal velocity:

Vt=2mgρACd−−−−−√

The mass term m appears here, and Vt is therefore proportional to it. So assuming that the objects have the same size and shape (and therefore the same drag coefficient and frontal area), but only different masses, the heavier object has a higher terminal velocity, and so will hit the ground first.