If a feather and a coin are dropped in a vacuum chamber:

Correct Option

The correct option is

Both fall with the same acceleration.

Explanation

The motion of objects in free fall is governed by the acceleration due to gravity. In the absence of external resistive forces such as air drag, this acceleration is constant for all bodies near the Earth's surface, regardless of their physical properties.

Detailed Analysis:
When objects are dropped in a vacuum chamber, air resistance is completely eliminated. The only force acting on the objects is the gravitational pull of the Earth. The acceleration due to gravity ($g$) is derived from Newton's Law of Universal Gravitation and is expressed as:

$$g = \frac{GM}{R^2}$$

Where:

• $G$ is the gravitational constant.
• $M$ is the mass of the Earth.
• $R$ is the radius of the Earth.

Crucially, this formula shows that acceleration due to gravity depends only on the mass of the source of gravity (Earth) and not on the mass, shape, or density of the falling object. Therefore, both the feather and the coin experience the same acceleration and, if dropped simultaneously from the same height, will hit the bottom at the same instant.

In a non-vacuum environment, the feather would fall slower due to air resistance acting against its relatively large surface area compared to its weight (buoyancy and drag). The vacuum removes this variable.

Key Takeaway:
In a vacuum, acceleration due to gravity is independent of the mass or shape of the falling body; thus, all objects fall at the same rate.