A large trolley is kept at rest on a frictionless horizontal surface. There are same peple standing on the trolley. Initially no one is moving.` C_(1)` is centre of mass of trolley and `C_(2)` is centre of mass of trolley plus people. Now people start moving on the trolley.

Options

A. Both `C_(1) and C_(2)` will be displaced with respect to ground.
B. Both `C_(1), and C_(2)` will remain at rest with respect to ground.
C. `C_(1)` will move but `C_(2)` will remain at rest with respect to ground
D. `C_(1)` will move but `C_(2)` will remain at rest with respect to ground

Explanation

To solve the problem, we need to analyze the motion of the trolley and the people standing on it, considering the concepts of center of mass (COM) and the effects of internal and external forces.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a large trolley on a frictionless horizontal surface with several people standing on it. Initially, both the trolley and the people are at rest.

2. **Identifying Centers of Mass**:
...