Two objects A and B of masses 2 kg and 20 kg are dropped from a height of 10 m simultaneously. Then

Options

A. both A and B experience same gravitational force.
B. the accelerations of both A and B are same.
C. both A and B reach the ground simultaneously.
D. both (b) and (c).

Explanation

To solve the question regarding the two objects A and B of masses 2 kg and 20 kg dropped from a height of 10 meters, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two objects, A (mass = 2 kg) and B (mass = 20 kg), both dropped from the same height of 10 meters.

2. **Gravitational Force**:
The gravitational force acting on an object is given by the formula:
\[ F = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
- For object A:
\[ F_A = 2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19.6 \, \text{N} \]
- For object B:
\[ F_B = 20 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 196 \, \text{N} \]
This shows that the gravitational force is different for both objects due to their different masses.

3. **Acceleration**:
According to the laws of physics, all objects in free fall experience the same acceleration due to gravity, regardless of their mass. This means:
\[ a_A = a_B = g = 9.8 \, \text{m/s}^2 \]
Therefore, the acceleration of both A and B is the same.

4. **Time to Reach the Ground**:
The time taken to fall from a height can be calculated using the formula:
\[ t = \sqrt{\frac{2h}{g}} \]
where \( h \) is the height (10 m) and \( g \) is the acceleration due to gravity.
- Substituting the values:
\[ t = \sqrt{\frac{2 \cdot 10 \, \text{m}}{9.8 \, \text{m/s}^2}} \approx \sqrt{\frac{20}{9.8}} \approx \sqrt{2.04} \approx 1.43 \, \text{s} \]
Both objects A and B will take approximately the same time to reach the ground since they are dropped from the same height and experience the same acceleration.

5. **Conclusion**:
- Both objects A and B experience the same gravitational acceleration.
- Both objects A and B will reach the ground simultaneously.

### Final Answer:
Both statements about the acceleration being the same and both objects reaching the ground simultaneously are correct. Therefore, the correct option is that both B and C are correct statements.

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