What will happen if we drop a stone and a feather together at the same time in a place where there is no air?

The Apollo 15 Hammer-Feather Drop:

At the end of the last Apollo 15 moon walk, Commander David Scott (pictured above) performed a live demonstration for the television cameras. He held out a geologic hammer and a feather and dropped them at the same time. Because they were essentially in a vacuum, there was no air resistance and the feather fell at the same rate as the hammer, as Galileo had concluded hundreds of years before – all objects released together fall at the same rate regardless of mass. Mission Controller Joe Allen described the demonstration in the “Apollo 15 Preliminary Science Report”:

During the final minutes of the third extravehicular activity, a short demonstration experiment was conducted. A heavy object (a 1.32-kg aluminum geological hammer) and a light object (a 0.03-kg falcon feather) were released simultaneously from approximately the same height (approximately 1.6 m) and were allowed to fall to the surface. Within the accuracy of the simultaneous release, the objects were observed to undergo the same acceleration and strike the lunar surface simultaneously, which was a result predicted by well-established theory, but a result nonetheless reassuring considering both the number of viewers that witnessed the experiment and the fact that the homeward journey was based critically on the validity of the particular theory being tested.

Thanks, @abcoetzee.

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This video was posted 1 decade ago.

Buzz Aldrin on the moon, 1969, NASA

Say you have two objects: a billiard ball and a feather. You drop both from the same height at the same time. You lay odds on the ball hitting the ground first -- and you're probably right, even if it's just by a split-second. However, as demonstrated by Galileo in 1589, mass does not affect gravitational pull; theoretically, all things should fall at the same rate, regardless of how heavy they are.

Back in 1971, on his last day on the moon, Apollo 15 Commander David Scott tested this theory. In one hand, he took a 1.32kg aluminium geological hammer. In his other, a 30g falcon feather, 44 times lighter than the hammer. Sure enough, when he dropped them both from the same height at the same time, they hit the ground simultaneously -- thus demonstrating Galileo's theory.

On Earth, it doesn't necessarily work this way. This is because the planet is enclosed in a bubble of gas -- the atmosphere -- which causes an effect called aerodynamic drag, particularly on objects that have a comparatively large surface area -- such as feathers or fabric. It is caused by the pressure of a medium, such as air, on a solid object. Every time you move, you are pushing against air. The denser the medium the object is moving through, the stronger the drag pressure -- which is why water is more difficult to move through than air. Aerodynamic drag is also what allows parachutes to work. The drag pressure across the surface area of the fabric is enough to slow descent to a safe speed. On the moon, there is no atmosphere -- and therefore no aerodynamic drag to slow the fall of high surface area objects. If you were to use a parachute on the moon, you'd end up looking pretty silly and possibly broken.

So why did Curiosity have a parachute? Mars, in fact, does have an atmosphere -- albeit a very thin one, made up mostly of carbon dioxide. Curiosity's parachute, about 51 feet (15.5 metres), is twice the size of a parachute that can safely drop a human on Earth -- and isn't considered safe for human missions, since a human-carrying spaceship will be a lot heavier than the Curiosity lander. To that end, NASA is currently developing what it is calling the Low-Density Supersonic Decelerator to be used in concert with a 110-foot-diameter (33.5 metres) parachute. The LDSD is a saucer-shaped inflatable designed to slow a craft while travelling at supersonic speeds through a low-density atmosphere.

And that's why Galileo was boss.

At the end of the last Apollo 15 moon walk, Commander David Scott (pictured above) performed a live demonstration for the television cameras. He held out a geologic hammer and a feather and dropped them at the same time. Because they were essentially in a vacuum, there was no air resistance and the feather fell at the same rate as the hammer, as Galileo had concluded hundreds of years before - all objects released together fall at the same rate regardless of mass. Mission Controller Joe Allen described the demonstration in the "Apollo 15 Preliminary Science Report":

"During the final minutes of the third extravehicular activity, a short demonstration experiment was conducted. A heavy object (a 1.32-kg aluminum geological hammer) and a light object (a 0.03-kg falcon feather) were released simultaneously from approximately the same height (approximately 1.6 m) and were allowed to fall to the surface. Within the accuracy of the simultaneous release, the objects were observed to undergo the same acceleration and strike the lunar surface simultaneously, which was a result predicted by well-established theory, but a result nonetheless reassuring considering both the number of viewers that witnessed the experiment and the fact that the homeward journey was based critically on the validity of the particular theory being tested." - Joe Allen, NASA SP-289, Apollo 15 Preliminary Science Report, Summary of Scientific Results, p. 2-11

Answer

Verified

Hint: To solve this question, we have to remember that air friction will work here as air resistance and the total force acting on the body will be equal to weight of the body – air friction.

Complete answer:

We have given that,A stone and a feather dropped from the same height do not reach the ground at the same time.and the given reason behind this assertion is that Acceleration due to gravity is dependent on the mass of the object.So,First, we will find out the force acting on the feather.Here, a downward force will act on the feather, whose magnitude will be equal to the weight of the feather, i.e.$w = mg$, where m is the mass of the feather and g is the acceleration due to gravity.Here, the air friction will work as air resistance for the feather,So, another force will also act on the feather which is opposite to the motion, i.e. upward force.Hence, the total force acting on the feather,$ \Rightarrow {F_{feather}} = $w – air friction.Similarly, we can find the total force acting on the stone.The downward force acting on the stone will be,$W = Mg$, where M is the mass of stone and g is the acceleration due to gravity.The upward force will be the air friction.So, the total force acting on the stone will be,$ \Rightarrow {F_{stone}} = $W – air friction.It is obvious that, mass of the stone is greater than the mass of feather, i.e. M > m.Therefore, W > w.Hence, ${F_{stone}} > {F_{feather}}$.

Now, we can say that the assertion is true but the reason, acceleration due to gravity is dependent on the mass of the object is false.

So, the correct answer is “Option C”.

Note:

When a body falls freely towards the surface of the earth, its velocity continuously increases. The acceleration developed in its motion is called acceleration due to gravity. When a body is in free fall, a gravitational pull mg does act on it. It is said to be weightless because it exerts no force on its support.