A planet is revolving around the sun in a circular orbit with a radius $$r$$. The time period is $$T$$. If the force between the planet and star is proportional to $$r^{-3 / 2}$$, then the square of time period is proportional to

The weight of a body on the surface of the earth is 63 N. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

A space ship is launched into a circular orbit close to earth’s surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull?

(Radius of earth = 6400 km, g = 9.8 m/s$$^2$$)

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth $$=R$$ )