At a certain distance from the center of the Earth, a 0.4-kg object has a weight of 2.0 N. (a) Find this distance. (b) If the object is released at this location and allowed to fall toward the Earth, what is its initial acceleration

a) The distance of the object from the center of the Earth is 8.92x10⁶ m.

b) The initial acceleration of the object is 5 m/s².

Explanation:

a) The distance can be found using the equation of gravitational force:

Where:

G: is the gravitational constant = 6.67x10⁻¹¹ Nm²/kg²

M: is the Earth's mass =  5.97x10²⁴ kg  

m: is the object's mass = 0.4 kg

F: is the force or the weight = 2.0 N    

r: is the distance =?

The distance is:

Hence, the distance of the object from the center of the Earth is 8.92x10⁶ m.

b) The initial acceleration of the object can be calculated knowing the weight:              

Where:            

W: is the weight = 2 N

a: is the initial acceleration =?          

Therefore, the initial acceleration of the object is 5 m/s².

I hope it helps you!