Two bodies one held 30 cm directly above the other are relased simultaneously and fall freely under gravity. After 2 sec their relative separation will be :

Options

A. 10 cm
B. 20 cm
C. 30 cm
D. zero

Answer

To solve the problem of finding the relative separation between two bodies falling freely under gravity after 2 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- We have two bodies: Body A is held 30 cm above Body B.
- Both bodies are released simultaneously and fall freely under the influence of gravity.

2. **Initial Separation**:
- The initial separation between the two bodies is 30 cm (0.3 meters).

3. **Equations of Motion**:
- Since both bodies are falling freely under gravity, we can use the equation of motion:
\[ S = ut + \frac{1}{2} a t^2 \]
- Where:
- \( S \) is the distance fallen,
- \( u \) is the initial velocity (which is 0 since they are dropped),
- \( a \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.

4. **Calculating the Distance Fallen by Each Body**:
- For both bodies, since they are dropped from rest, the initial velocity \( u = 0 \).
- The distance fallen by each body after \( t = 2 \) seconds can be calculated as follows:
\[ S = 0 + \frac{1}{2} g t^2 \]
- Substituting \( g = 9.8 \, \text{m/s}^2 \) and \( t = 2 \, \text{s} \):
\[ S = \frac{1}{2} \times 9.8 \times (2)^2 = \frac{1}{2} \times 9.8 \times 4 = 19.6 \, \text{m} \]

5. **Distance Fallen by Each Body**:
- Both Body A and Body B fall the same distance of 19.6 meters after 2 seconds.

6. **Finding the Relative Separation**:
- Initially, the separation was 30 cm (0.3 m).
- After 2 seconds, both bodies have fallen the same distance (19.6 m).
- Therefore, the relative separation remains unchanged:
\[ \text{Relative Separation} = \text{Initial Separation} = 30 \, \text{cm} \, (0.3 \, \text{m}) \]

### Final Answer:
The relative separation between the two bodies after 2 seconds is **30 cm**.