A particle hanging form a spring stretches it by 1 cm at earth's surface. How much will the same particle stretch the spring at a place 800 km above the earth's surface? Radius of the earth=6400 km.

Explanation

To solve the problem, we need to determine how much a particle will stretch a spring when it is located 800 km above the Earth's surface, given that it stretches the spring by 1 cm at the Earth's surface.

### Step-by-Step Solution:

1. **Understand the Forces at Play**:
At the Earth's surface, the gravitational force acting on the particle is balanced by the spring force. The gravitational force \( F_g \) can be expressed as:
\[
F_g = \frac{GMm}{R^2}
...