Gravitation PYQs - Last 5 Years

Find gravitational field at a distance of \(2000 \mathrm{~km}\) from the centre of earth. (Given
\(R_{\text {earth }}=6400 \mathrm{~km}, r=2000 \mathrm{~km} \text {, } M_{\text {earth }}=6 \times 10^{24} \mathrm{~kg} \text { ) }\)

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 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

Two satellites \(A\) and \(B\) revolve round the same planet in coplanar circular orbits lying in the same plane. Their periods of revolutions are \(1 \mathrm{~h}\) and \(8 \mathrm{~h}\), respectively. The radius of the orbit of \(A\) is $$...

Two satellites \(S_1\) and \(S_2\) are revolving round a planet in coplanar circular orbits of radii \(r_1\) and \(r_2\) in the same direction, respectively. Their respective periods of revolution are \(1 \mathrm{~h}\) and \(8 \mathrm{~h}\)...

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 \(=R\) )

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\(^2\))