A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface.If this object is moved 500 km farther from the planet,the gravitational force on it will be closest to
A) 75 N.
B) 71 N.
C) 56 N.
D) 50 N.
E) 25 N.

Question

Quizplus · Accepted Answer

The gravitational force F between two objects of masses M and m, separated by a distance r is given by:

F = (G*M*m)/(r^2)

Where G is the gravitational constant.

Since the mass of the object is not given, we can assume it to be small compared to the mass of the planet. Thus, we can consider only the mass of the planet.

Using the given values, we can find the mass of the planet:

100 N = (G*M*m)/(500 + 1000)^2
M = 6.67*10^-11 * 100 * (1500)^2 / (1000^2)
M = 1.125*10^17 kg

Now, if the object is moved 500 km farther from the planet, the new distance from the center of the planet will be 1500 km. Plugging this value into the gravitational force equation, we get:

F = (G*M*m)/(1500^2)
F = 4.44*10^11 N*m^2/kg^2 * 100 * 1.125*10^17 / (1500^2)
F = 56 N (approx)

Therefore, the choice closest to the calculated value is C) 56 N.

A Small Planet Having a Radius of 1000 Km Exerts