Gravitation - Mechanics - Physics Previous Year Questions

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 2%, its speed will increase by

Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

If the earth stops rotating about its axis, then what will be the change in the value of g at a place in the equatorial plane? (Radius of earth = 6400 km)

From a solid sphere of mass M and radius R, a spherical portion of radius \({R \over 2}\) is removed as shown in the figure.

Taking gravitational potential V = 0 at r = \(\infty\), the potential at the centre of the cavity thus formed is

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

A man of mass $m$ starts falling towards a planet of mass \(M\) and radius \(R\). As he reaches near to the surface, he realizes that will pass through a small role in the planet. As he enters the role, we sees that the planet is really made of two pieces a spherical shell of negligible thickness of mass \(3 M / 4\) and a point mass \(M / 4\) at the centre. Change in the force of gravity experienced by the man is

A body is projected vertically upwards from the surface of Earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be

A mass $M$ is broken into two parts of masses $m_1$ and $m_2$. How are $m_1$ and $m_2$ related, so that force of gravitational attraction between the two parts is maximum?