A tunnel is dug along a diameter if the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the center.

Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.

What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the North Pole?

A mass m is placed at P a distance h along the normal through the centre O of a thin circular ring of mass M and radius r (Fig. 8.3).

If the mass is removed further away such that OP becomes 2h, by what factor the force of gravitation will decrease, if h = r?

Molecules in air in the atmosphere are attracted by gravitational force of the earth. Explain why all of them do not fall into the earth just like an apple falling from a tree.

How is the gravitational force between two - point masses affected when they are dipped in water keeping the separation between them the same?

The gravitational force between a hollow spherical shell (of radius R and uniform density) and a point mass is F. Show the nature of F vs r graph where r is the distance of the point from the centre of the hollow spherical shell of uniform density.

We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in figure (11-E3). The point A is the Centre of the plane section of the first part and B is the Centre of the place section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.

A uniform metal sphere of radius α and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4α (figure 11-E2). The Centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P₁ and P₂ shown in the figure.