What can be said about the centre of mass f a uniform hemisphere without making any calculation? Wil its distance from the centre be more thn r/2 or less than r/2?

A particle of mass m was transferred from the centre of the base of a uniform hemisphere of mass M and radius R into infinity. What work was performed in the process by the gravitational force exerted on the particle by the hemisphere?

Calculate the gravitational potential at the centre of base of a solid hemisphere of mass M , radius R .

A cavity of radius R//2 is made inside a solid sphere of radius R . The centre of the cavity is located at a distance R//2 from the centre of the sphere. The gravitational force on a particle of a mass 'm' at a distance R//2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity). [Here g=GM//R^(2) , where M is the mass of the solide sphere]

The electric field at a distance (3R)/2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the centre of the sphere is :

A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P a distance R/2 from the centre of the shell is

Distance of the centre of mass of a solid uniform cone from its vertex is z_0 . It the radius of its base is R and its height is h then z_0 is equal to:

A double star is a system of two stars of masses m and 2m , rotating about their centre of mass only under their mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to

A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance r (r gt R) from the center of the sphere. Find the minimum velocity v so that it can penetrate (R//2) distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere of radius R and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?