Gravitation - Mechanics - Physics Previous Year Questions

A skylab or mass \(m \mathrm{~kg}\) is first launched from the surface of the earth in a circular orbit of radius \(2 R\) (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius \(3 R\). The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are

A geostationary satellite revolves around the Earth in a circular orbit of radius \(4 R\). Here, $R$ is the radius of the Earth. Then, the time period of another satellite moving in a circular orbit of radius \(2 R\) is:

The gravitational field in a region is given by \(\mathbf{E}=5 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{i}}+12 \mathrm{~N} / \mathrm{kg} \hat{\mathbf{j}}\). The change in the gravitational potential energy of a particle of mass \(1 \mathrm{~kg}\) when it is taken from the origin to a point (\(5 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}\)) is

The distance of the centres of Moon and the Earth is $D$. The mass of the Earth is 81 times the mass of the Moon. At what distance from the centre of the Earth, the gravitational force on a particle will be zero?

If gravitational attraction between two points masses be given by $F=G \frac{m_1 m_2}{r^n}$, then the period of a satellite in a circular orbit will be proportional to