The distance from the center of the earth to a point where the acceleration due to gravity is g/16 is

none of the these.
4RE.
3RE.
16RE.
1/4RE.

If one goes 4 RE, then gravity will be

F=GMm/(4re)^2

I don't know what that means. Can you explain?

I wonder if you know what g is...

F=GMm/re^2 at radius earth
F/m= g= GM/re^2

if you go out 4 re, then

F/m= GM/16re^2= g/16

To find the distance from the center of the Earth to a point where the acceleration due to gravity is g/16, we can use Newton's law of universal gravitation.

According to Newton's law of universal gravitation, the acceleration due to gravity at a distance r from the center of the Earth is given by the equation:

g = (GM) / r^2

Where:
g is the acceleration due to gravity (g = 9.8 m/s^2)
G is the gravitational constant (G = 6.674 × 10^-11 N m^2/kg^2)
M is the mass of the Earth (M = 5.972 × 10^24 kg)
r is the distance from the center of the Earth

We need to solve for r in terms of g.

Rearranging the equation, we have:

r^2 = (GM) / g

Taking the square root of both sides, we get:

r = sqrt((GM) / g)

Substituting the given value of acceleration due to gravity, g/16, we get:

r = sqrt((GM) / (g/16))

Simplifying further, we have:

r = sqrt(16GM / g)

Now, let's substitute the values for G and M:

r = sqrt((16 × 6.674 × 10^-11 N m^2/kg^2 × 5.972 × 10^24 kg) / (g))

Simplifying, we get:

r = sqrt(106.784 × 10^13 N m^2/kg) / (g)

r = sqrt(106.784 × 10^13) / (g)

r = (10.336 × 10^6 m) / (g)

Therefore, the distance from the center of the Earth to a point where the acceleration due to gravity is g/16 is 10.336 × 10^6 meters divided by the given acceleration due to gravity g.