Hemisphere

A beam of diameter 'd' is incident on a glass hemisphere as shown in the figure. If the radius of curvature of the hemisphere is very large in comparision to d, then the diameter of the beam at the base of the hemisphere will be:

A beam of diameter 'd' is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be

A beam of diameter 'd' is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be :

Two solid hemispheres of radii R and (R )/(2) with centers O and O' respectively as shown in figure. The density of bigger hemisphere is rho and that of smaller hemisphere is 2rho . Taking center of bigger hemisphere is at origin and the distance between centres of two hemisphere OO' is (R)/(10) find co - ordinates of center of mass of the system.

A chain of length l and mass m lies of the surface of a smooth hemisphere of radius Rgtl with one end tied to the top of the hemisphere. Taking base of the hemisphere as reference line, find the gravitational potential energy of the chain.

A cube is inscribed in a hemisphere of radius R, such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the half-sphere. What is the volume of the cube?

A smooth hemisphere of mass M is kept on a smooth surface. A block of mass m ( = M//3) is kept on the top of the hemisphere as shown in the figure. The hemisphere is displaced slightly ang both the hemisphere and the block starts moving. At an angle theta with the vertical ( subtended by the block at the centre of the hemisphere ) , the relation between the velocity of the block ( V) and the velocity of the hemishere ( v_(0) ) is (V is the velocity of the block w.r.t. the hemisphere at that instant . )