Final answer:
The question asked for the distance from the Earth's center where a 4.0 kg object weighs 4.0 N. The answer involves the concept of weight expressed by the formula w = mg, and the calculation of the distance using Newton's law of universal gravitation, but the provided options do not align with the details required for a precise calculation under ideal conditions.
Step-by-step explanation:
The student's question seeks to determine the distance from the center of the Earth at which a 4.0 kg object has a weight of 4.0 N. Given that the standard acceleration due to gravity (g) is 9.80 m/s², we start by using the formula for weight (w = mg) and solve for the value of g that would result in a 4.0 N weight for a 4.0 kg object:
w = mg
4.0 N = (4.0 kg)(g)
g = 1.0 m/s²
Next, we can use the formula that relates gravitational force to the masses involved and the distance between them, Newton's law of universal gravitation:
F = G(m1*m2)/r²
Where F is the gravitational force (or weight), G is the gravitational constant (6.674×10⁻¹¹ Nm²/kg²), m1 and m2 are the masses of the objects, and r is the distance between their centers. Plugging in known values, we have the weight (F) of 4.0 N, mass of the object (m2) of 4.0 kg, mass of Earth (m1) of 5.971×10¹¹ kg, and the gravitational constant (G). We solve for r, the distance from the Earth's center.
Since the exact distance calculation requires complex operations and can't be accurately represented with the options provided (A, B, C, D), the problem seems to have insufficient data or might be assumptive. Therefore, we cannot derive the precise answer given the options presented. The concept of weight and distance from the center of Earth indicates that as an object moves away from Earth, its weight will decrease due to the inverse square law of gravity, which states that gravitational force decreases with the square of the distance from the source.