Understanding the Concepts

* Weight: Weight is the force of gravity acting on an object's mass. It depends on the object's mass and the gravitational acceleration.

* Gravitational Force: The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Setting up the Problem

Let:

* *m* = mass of the object

* *g* = acceleration due to gravity at the Earth's surface

* *r* = radius of the Earth

* *h* = distance from the Earth's surface to the point where the weight is 50 N

* *G* = gravitational constant

Calculations

1. Weight at the surface:

* 200 N = *m* *g*

2. Weight at a distance h from the surface:

* 50 N = *m* *G* *M / (r + h)² (where *M* is the mass of the Earth)

3. Ratio of Weights:

* Divide the equation for weight at distance *h* by the equation for weight at the surface:

(50 N) / (200 N) = (*G* *M* / (r + h)²) / (*g*)

* Simplify: 1/4 = (r² / (r + h)²)

4. Solving for h:

* Take the square root of both sides: 1/2 = r / (r + h)

* Cross-multiply: r + h = 2r

* Solve for h: h = r

Answer:

The object will weigh 50 N at a distance r (the radius of the Earth) from the center of the Earth. In other words, the weight will be 50 N at a point on the surface of the Earth.