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 closest to A) 71 N. B) 25 N. C) 56 N. D) 50 N. E) 75 N.

Answer 1

Option C is the correct answer.

Explanation:

Gravitational force is given by

                  $F=\frac{GMm}{r^2}$

         G=6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²

         M = Mass of object 1

          m = mass of object 2

          r = Distance between objects.

Here only variable is r value.

In case 1

             $100=\frac{GMm}{(1000+500)^2}\\\\GMm=100\times 1500^2$

In case 2

            $F=\frac{GMm}{(1000+500+500)^2}\\\\F=\frac{GMm}{2000^2}\\\\F=\frac{100\times 1500^2}{2000^2}\\\\F=56.25N$

Option C is the correct answer.