If two object are free to fall at same time than both object reaches the ground at the same time becoz gravity acting on both object is same n as there is vacuum so the weight of doesn't matters....

Introduction:
When two objects of different masses are dropped from the same height in a vacuum, the question arises whether there will be any difference in the time taken by each object to reach the ground. This can be analyzed using the principles of free fall and gravitational acceleration.

Principle of free fall:
In the absence of air resistance, all objects near the surface of the Earth experience the same acceleration due to gravity, denoted by 'g'. This acceleration is approximately 9.8 m/s^2.

Analysis:
To determine whether there will be any difference in the time taken by the two objects to reach the ground, we need to consider the factors influencing their motion.

1. Gravitational force:
Both objects experience the same gravitational force since they are dropped from the same height and are equally affected by the Earth's gravitational pull. The gravitational force acting on an object is given by F = mg, where 'm' is the mass of the object and 'g' is the acceleration due to gravity.

2. Acceleration:
As mentioned earlier, both objects experience the same acceleration due to gravity. Therefore, the rate at which their velocities change is equal, regardless of their masses.

3. Time of fall:
The time taken for an object to fall can be calculated using the equation t = √(2h/g), where 'h' is the initial height and 'g' is the acceleration due to gravity.

Conclusion:
Based on the analysis, it can be concluded that the masses of the objects do not affect the time taken for them to reach the ground. The only factors influencing the time of fall are the height from which they are dropped and the acceleration due to gravity. Therefore, both objects will reach the ground at the same time in a vacuum, regardless of their masses.