A solid sphere of radius R has a mass distributed in its volume of mass density `rho=rho_(0)` r, where `rho_(0)` is constant and r is distance from centre. Then moment of inertia about its diameter is

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

A solid sphere of radius R has a charge Q distributed in its volume with a charge density rho=kr^a , where k and a are constants and r is the distance from its centre. If the electric field at r=(R)/(2) is 1/8 times that r=R , find the value of a.

A solid sphere of radius R has a volume charge density rho=rho_(0) r^(2) (where rho_(0) is a constant ans r is the distance from centre). At a distance x from its centre (for x lt R ), the electric field is directly proportional to :

A non-conducting solid sphere has volume charge density that varies as rho=rho_(0) r, where rho_(0) is a constant and r is distance from centre. Find out electric field intensities at following positions. (i) r lt R" " (ii) r ge R

If rho is density of the material of a sphere of radius R . Then its moment of inertia about its diameter is

A thin circular plate of mass M and radius R has its density varying as rho(r)=rho_(0)r with rho_0 as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = aMR^(2) The value of the coefficient a is :

[" A solid sphere of radius "R" is charged with "],[" volume charge density "rho=Kr^(n)," where "K" and "n],[" are constants and "r" is the distance from its "],[" centre.If electric field inside the sphere at "],[" distance "r" is proportional to "r^(4)," then find the "],[" value of "n.]