Two balls of same size but the density of one is greater than that of the other are dropped from the same height, then which ball will reach the earth first (air resistance is negligible)

Options

A. Heavy ball
B. Light ball
C. Both simultaneously
D. Will depend upon the density of the balls

Explanation

To solve the problem of which ball will reach the ground first when two balls of the same size but different densities are dropped from the same height (with negligible air resistance), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have two balls of the same size but different densities. One ball has a higher density than the other. We need to determine which ball reaches the ground first when dropped from the same height.

2. **Identify the Key Factors**: The two main factors affecting the motion of the balls are:
- The height from which they are dropped (same for both).
- The acceleration due to gravity (g), which is constant for both balls.

3. **Apply the Laws of Motion**: According to the second equation of motion, the distance fallen by an object under gravity can be expressed as:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \(s\) is the distance fallen (height),
- \(u\) is the initial velocity (0 for both balls since they are dropped),
- \(a\) is the acceleration (which is \(g\) for both).

4. **Set Up the Equation**: Since both balls are dropped from rest (initial velocity \(u = 0\)), the equation simplifies to:
\[ h = \frac{1}{2} g t^2 \]
Rearranging gives:
\[ t^2 = \frac{2h}{g} \]
Taking the square root:
\[ t = \sqrt{\frac{2h}{g}} \]

5. **Analyze the Results**: The time \(t\) it takes for each ball to reach the ground depends only on the height \(h\) and the acceleration due to gravity \(g\). Importantly, it does not depend on the mass or density of the balls.

6. **Conclusion**: Since both balls are dropped from the same height and experience the same gravitational acceleration, they will both reach the ground at the same time, regardless of their densities.

### Final Answer:
Both balls will reach the ground at the same time.

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