Question

A stone of mass 2 kg takes 4 s to reach the ground when it is dropped from a tower. What is the time taken by another stone of mass 4 kg for the same fall?​

Answer 1

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If you ignore the air resistance, both objects would fall at the same time (Galileo's law)

Answer 2

Answer:

The time taken by the stone of mass 4 kg will be 4 seconds.

Explanation:

• We know that time never depends on mass and it is an independent quantity.
• The following calculations can prove the independence of time.

In the question we are given the following data:

1. Mass of 1st stone - 2 kg
2. Mass of 2nd stone - 4 kg
3. Time taken for 1st stone - 4 s

We use the following formula to find the distance covered by the 1st stone.

S = $\frac{1}{2}$ × g × t²

Where,

1. S = Distance covered
2. g = accerelation due to gravity (10m/s²)
3. t = time taken

Substituting the values of 1st stone:

S = $\frac{1}{2}$ × 10 × 4²

S = $\frac{1}{2}$ × 10 × 16

S = 5 × 16

S = 80 m

The distance traveled by the 2nd stone will be the same. We will use the same formula to calculate the time taken.

80 = $\frac{1}{2}$ × 10 × t²

80 × 2 = 10 × t²

160 = 10 × t²

$\frac{160}{10}$ = t²

16 = t²

$\sqrt{16}$ = t

4 s = t

We can see that the time taken by the 2nd stone is the same.

Conclusion:

It takes 4 seconds for the stone of 4 kg to hit the ground as time is independent of mass.