In a vacuum, a five-rupee coin, a feather of a sparrow bird and a mango are dropped simultaneously from the same height. The time taken by them to reach the bottom is t|, tg and tg respectively. In this situation, we will observe that

In a vacuum, the only force acting on a falling object is gravity, as air resistance is absent. According to the principles of free fall established by Galileo, the acceleration due to gravity (g) is constant for all objects regardless of their mass, density, or shape. The time taken (t) to fall from a height (h) is determined by the formula h = 1/2gt", which simplifies to t = √(2h/g). Since the five-rupee coin, the sparrow feather, and the mango are dropped from the same height in a vacuum, they all experience the same acceleration (g ≈ 9.8 m/s") and will reach the bottom simultaneously. Therefore, the time taken by each object is equal, resulting in the relationship t1 = t2 = t3.