Question

How can you account for the fact that a stone and a feather fall at the same rate in vacuum but at different rate in air ?

Answer 1

Free fall in case of vacuum:

1. A freely falling body means when a body falls down towards the center of the earth under the influence of a single force, which is the gravitational pull of the earth.
2. Acceleration due to gravity $\text{'}g\text{'}$is the acceleration of a body due to the gravitational force of attraction acting on the body.
3. The acceleration is the same for all bodies when air is not present.
4. In a vacuum, all the freely falling bodies have the same acceleration which is equal to $\text{'}g\text{'}$.
5. According to the first equation of motion, $v=u+gt$, where $u$is the initial velocity, $v$ is the final velocity, $t$ is the time taken.
6. For the freely falling bodies, $u=0$, thus, $v=gtort=\frac{v}{g}$.
7. The time taken to reach the ground does not depends upon the mass, size, or area of the body, thus, the feather and stone reach the ground at the same time in the vacuum irrespective of their different forms.

Freefall in the presence of air,

1. In the air, the resistance may make the acceleration different for stone and feather.
2. Air resistance depends on the surface area and velocity.
3. As the feather has more surface area than the stone thus air resistance is more on the feather which causes the feather to fall more slowly than the stone.

Hence, a stone and a feather fall at the same rate in a vacuum due to the same acceleration $\text{'}g\text{'}$. But in the air, a stone and a feather fall at a different rates due to air resistance.