A transparent sphere of radius R ahs a cavity of radius `R//2` as shown in figure,. Find the refractive index of the sphere if a parallel beam of light falling on left sureface focuses at point P.

A solid sphere having radius R and uniform charge density rho has a cavity of radius R/2 as shown in figure.Find the value of |E_A /E_B|

Three solid spheres of mass M and radius R are placed in contact as shown in figure. Find the potential energy of the system ?

A sphere of radius 2R and mas M has a spherical cavity of radius R as shown in the figure. Find the value of gravitational field at a point P at a distance of 6R from centre of the sphere.

Inside a uniform sphere of mass M and radius R, a cavity of radius R//3 , is made in the sphere as shown :

A non-conducting sphere of radius R has a spherical cavity of radius R//2 as shown. The solid part of the sphere has a uniform volume charge density rho . Find the magnitude and direction of electric field at point (a) O and (b) A.

A clear transparent glass sphere (mu=1.5) of radius R is immersed in a liquid of refractive index 1.25. A parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

A ray of light falls on a transparent sphere with centre at C as shown in figure. The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is

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