IIT JEE PROBLEM: A cavity of radius r is present inside a solid dielectric sphere of radius R

A cavity of radius r is present inside a fixed solid dielectric sphere of radius R, having a volume charge density of rho . The distance between the centres of the sphere and the cavity is a. An electron is released inside the cavity at an angle theta = 450 as shown. The electron (of mass m and charge –e) will take ((Psqrt(2)mrepsilon_(0))/(earho))^(1//2) time to touc the sphere again. Neglect gravity. find the value of P:

A point charge 'Q' is placed at the centre of a spherical cavity of radius 'b' carved inside a solid conducting sphere of radius 'a'. Then total energy of the system is: [k = (1)/(4pi in_(0))]

A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . They y -coordinate of the centre of mass of the remaining sphere is

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]

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 figure represents a solid uniform sphere of mass M and radius R . A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

A cavity of radius r is made inside a solid sphere. The volume charge density of the remaining sphere is rho . An electron (charge e, mass m) is released inside the cavity from point P as shown in figure. The centre of sphere and center of cavity are separated by a distance a. The time after which the electron again touches the sphere is

The radius of gyration of a solid sphere of radius R about its tangent is

A sphere of radius R and charge Q is placed inside an imaginary sphere of radius 2R whose centre coincides with the given sphere. The flux related to imaginary sphere is:

A hollow sphere of radius r is put inside another hollow sphere of radius R. The charges on the two are +Q and -q as shown in the figure. A point P is located at a distance x from the common centre such that r lt x lt R . The potential at the point P is