Two stones of different masses are dropped simultaneously from the top of a building

Options

A. Smaller stone hit the ground earlier
B. Larger stone hit the ground earlier
C. Both stones reach the ground simultaneously
D. Which of the stones reach the ground earlier depends on the

Answer

To solve the problem of two stones of different masses being dropped simultaneously from the top of a building, we can analyze the motion of the stones using the equations of motion under the influence of gravity.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have two stones, one with mass \( M_1 \) and the other with mass \( M_2 \).
- Both stones are dropped from the same height \( H \) at the same time.

2. **Identifying the Forces**:
- Both stones are acted upon by gravity, which accelerates them downwards. The acceleration due to gravity is denoted as \( g \).
- The mass of the stones does not affect the acceleration due to gravity; both stones will experience the same gravitational acceleration.

3. **Using the Equations of Motion**:
- The equation of motion for an object under uniform acceleration is given by:
\[ H = ut + \frac{1}{2} a t^2 \]
- Here, \( u \) (initial velocity) is 0 since the stones are dropped, and \( a \) is \( g \) (acceleration due to gravity).
- Thus, the equation simplifies to:
\[ H = 0 \cdot t + \frac{1}{2} g t^2 \implies H = \frac{1}{2} g t^2 \]

4. **Solving for Time**:
- Rearranging the equation to solve for time \( t \):
\[ t^2 = \frac{2H}{g} \implies t = \sqrt{\frac{2H}{g}} \]
- This equation shows that the time \( t \) taken to reach the ground depends only on the height \( H \) and the acceleration due to gravity \( g \), and is independent of the mass of the stones.

5. **Conclusion**:
- Since both stones are dropped simultaneously from the same height and experience the same gravitational acceleration, they will hit the ground at the same time, regardless of their masses.

### Final Answer:
Both stones reach the ground simultaneously.