A gas in a sphere of radius 2r is transferred to another sphere of radius r. Find the pressure after transferring if initial pressure is P.

The volume of a sphere of radius 2r is

Height of greatest cone inscribed in a sphere of radius r is

A Sphere of radius R_0 carries a volume charge density proportional to the distance (x) from the origin, rho=alphax where alpha is a positive constant. (a) Calculate the total charge in the sphere of radius R_0 . (b) The sphere is shaved off so as to reduce its radius. What should be the radius (R) of the remaining sphere so that it contains half the charge of the original sphere? (c) Find the electric field at a point inside the sphere at a distance r lt R. Give your answer for original sphere of radius R_0 as well as for the smaller sphere of radius R that was left after shaving off the original sphere.

Find the number of sphere of radius r touching the coordinate axes.

A conducting sphere of radius r has a charge . Then .

There is a gas in a sphere of radius 2r at a pressure P. If the same amount of gas is present in another sphere of radius r at same temperature, find its pressure.

A solid sphere of radius r is melted and recast into the shape of a solid cone of height r. Find radius of the base of the cone.

A hollow sphere of radius 2R is charged to V volts and another smaller sphere of radius R is charged to V/2 volts. Now the smaller sphere is placed inside the bigger sphere without changing the net charge on each sphere. The potential difference between the two spheres would be