Question

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

Answer 1

56.25 N

Step-by-step explanation:

Given,

Radius of the planet, r = 1000 km

Gravitational force, F = 100 N

Initial distance from the planet, d = 500 km

Final distance from the planet, D = 1000 km

Lets assume, mass of planet = M

mass of the object = m.

As per the gravitational law, the force due to gravity is given as

`F = (G * M * m)/(R^(2))`

where, G = gravitational constant

R = distance between the two objects.

Case 1: when the object is at a distance of 500 km from the planet,

`F = (G * M * m)/(R^(2)) = 100`

Here, R = 1000 + 500 = 1500 km, so

`(G * M * m)/(1500^(2)) = 100`

`G * M * m = 100 * {1500^(2)`

Case 2: when the object is at a distance of 1000 km from the planet, so

now, R = 1000 + 1000 = 2000 km

Now the gravitational force, F' will be

`F' = (G * M * m)/(R^(2))`

`F' = (100 * 1500^(2) )/(2000^(2))`

`F' = 56.25 N`

Thus, the gravitational force will now be reduced to 56.25 N.