Chapter 6, Problem 46A

In a vacuum, a coin and a feather fall side by side. Would it be correct to say that in a vacuum equal forces of gravity act on both the coin and the feather?

To determine

Whether the force acting on the coin and feather when they fall in vacuum is equal or not.

Answer to Problem 46A

Force exerted on the feather and coin in vacuum is different while their weight to mass ratiois same.

Explanation of Solution

Introduction:

In vacuum there is no equal force of gravity acts on the feather and coin. Only equal quantity in vacuum for feather and coin is the constant acceleration due to gravity. Due to this reason feather and coin fall side by side in vacuum.

Feather and coins experiment in the vacuum is very famous experiments since from long time. People really wonder about the nature of gravity when such kinds of experiment done. Vacuum is used for this experiment. Due to vacuum, there is no air molecule present which is responsible for drag force.

Since these two bodies fall under the gravity, this is the example of free fall. Force experience by the feather due to gravity is,

  $\therefore F_f=m_{f}g$ in the downward direction.

Similarly force experienced by the coin due to gravity is,

  $\therefore F_c=m_{c}g$

Where,

m_fand m_c are the masses of feather and coin respectively.

g- Acceleration due to gravity= 9.8 m/s²

Since masses of both the objects are different.

  $\therefore m_f\ne m_{\text{c}}$

Hence due to unequal masses force due to gravity exerted on the feather and coin is different. Only constant quantity in both the case is ratio of their weight to mass.

But the reason behind the side by side fall of coin and feather is the constant acceleration of both the body. In vacuum there is no air molecule present. So there is no drag force experience by both bodies. Acceleration is the time rate of change of velocity with respect to time. Since in vacuum velocity change for both feather and coin is same for a given time interval. Due to that reason feather and coin fall in vacuum side by side.

Conclusion:

Hence due to unequal masses force due to gravity exerted on the feather and coin is different. Only constant quantity in both the case is ratio of their weight to mass.