Answer:
56.25 N
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
[tex]F = \frac{G \times M \times m}{R^{2}}[/tex]
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,
[tex]F = \frac{G \times M \times m}{R^{2}} = 100[/tex]
Here, R = 1000 + 500 = 1500 km, so
[tex]\frac{G \times M \times m}{1500^{2}} = 100[/tex]
[tex]G \times M \times m = 100 \times {1500^{2}[/tex]
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
[tex]F' = \frac{G \times M \times m}{R^{2}}[/tex]
[tex]F' = \frac{100 \times 1500^{2} }{2000^{2}}[/tex]
[tex]F' = 56.25 N[/tex]
Thus, the gravitational force will now be reduced to 56.25 N.
