Introduction:
The weight of an object is the force exerted on it due to gravity. It is directly proportional to the mass of the object and the acceleration due to gravity. As we move away from the surface of the Earth, the force of gravity decreases, resulting in a decrease in weight. In this response, we will determine at what height above the surface of the Earth the weight of a body will be 1/4th of what it is on the surface.

Determining the height:
To find the height at which the weight of the body is 1/4th of its weight on the surface, we can use the inverse square law of gravity. According to this law, the force of gravity decreases with the square of the distance. Therefore, the weight of the body at a certain height h above the surface can be calculated using the following equation:

Weight at height h = Weight on the surface × (R / (R + h))^2

Where R is the radius of the Earth and h is the height above the surface.

Calculating the height:
We need to find the height at which the weight is 1/4th of its value on the surface. Let's denote the weight on the surface as W0. According to the equation above, the weight at height h is given by:

Weight at height h = W0 × (R / (R + h))^2

We can rearrange this equation to solve for h:

h = R × (√(W0/4) - 1)

Substituting values:
To calculate the height, we need to know the radius of the Earth and the weight on the surface. The radius of the Earth is approximately 6,371 kilometers (or 6,371,000 meters). Let's assume the weight on the surface is 100 units for simplicity.

Substituting these values into the equation:

h = 6,371,000 × (√(100/4) - 1)
h = 6,371,000 × (5 - 1)
h = 6,371,000 × 4
h = 25,484,000 meters

Conclusion:
Therefore, the height above the surface of the Earth at which the weight of the body will be 1/4th of its weight on the surface is approximately 25,484,000 meters.

I guess it will be 16Rsq.