Question

Two metal balls are the same size, but one weighs twice as much as the other. The balls are dropped from the top of a two story building at the same instant of time. The time it takes the balls to reach the ground below will be:

Answer 1

The time taken by the metal balls of the same size but different weight, to reach the ground will be the same.

Reason behind:

Two metal balls are the same size, but one weighs twice as much as the other. The balls are dropped from the top of a two-story building at the same instant of time. It is required to find the time taken by the balls to reach the ground.

In free fall, all objects experience the same acceleration owing to gravity when they are close to the earth.

$g=9.8 \text{ m/s}^2$ is the measure of gravitational acceleration.

Because of this, the two metal balls are the same size but have different masses. The air resistance for both balls will be the same due to their similar sizes. Let, g' be the acceleration in the presence of air resistance. The balls are both discharged at once.

From a height of h, both balls descend due to gravity G'.

Therefore, the time taken by both balls is:

$\begin{aligned}&s=u t+\frac{1}{2} g t^{2} \\&u=0, s=h \\&t=\sqrt{\frac{2 h}{g}}\end{aligned}$

Therefore, the time is independent of mass. Thus the time taken by both the balls, will be about the same.

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