At what distance from the center of the Earth would one's weight be half that recorded on the Earth's surface? Let the Earth's radius be R.
A) 0.71R
B) 2R
C) 4R
D) 1.4R

Question

Quizplus · Accepted Answer

The weight of an object at any distance d from the center of the Earth is given by W = mg, where m is the mass of the object and g is the acceleration due to gravity at that distance. 
On the Earth's surface, the weight is W1 = mg1, where g1 is the acceleration due to gravity at the surface. 
To find the distance where weight is half, we can set W = W1 / 2: 
mg = (mg1) / 2 
Simplifying, we get: 
g / g1 = 1 / 2 
g = (GME) / d^2 
g1 = (GME) / R^2 
Substituting these values and solving for d, we get: 
d = sqrt(2) * R or d = -sqrt(2) * R (negative root does not make physical sense) 
Therefore, the distance would be 1.4 times the Earth's radius or d=1.4R.

At What Distance from the Center of the Earth Would