Consider the shown uniform solid insulating sphere of mass m with a short and light electric dipole moment `p hat(j)` embedded at its centre placed at rest on a horizontal surface. An electric field `E hat(i)` is suddenly switched on in the region such that the sphere starts ro/ling without sliding. Speed of the sphere when the dipole becomes horizontal for the first time is given as:

A non conducting solid sphere of mass m and radius R having uniform charge density +rho and -rho as shown in figure. It is then placed on a rough non conducting horizontal plane. At t=0 a uniform electric field vecE=E_(0)hati N//C is switched on and the solid sphere starts rolling with sliding. The magnitude of frictional force at t=0 is (2rhopiR^(3)E_(0))/K . Find the value of K

A nonconducting ring of mass m and radius R is charged as shown. The charged density i.e. charge per unit length is lambda . It is then placed on a rough nonconducting horizontal surface plane. At time t = 0, a uniform electric field vecE=E_(0)hati is switched on and the ring starts rolling without sliding. The friction force (magnitude and direction) acting on the ring, when it starts moving is

A nonconducting ring of mass m and radius R, with charge per unit length lambda is shown in fig. It is then placed on a rough nonconducting horizontal plane. At time t=0, a uniform electric field vecE =E_(0)hati is switched on and the ring starts rolling without on and the ring starts rolling without sliding. Determine the friction froce (magnitude and direction ) acting on the ring.

A solid cylinder of mass m, length l and carrying a current 'i' is placed on two rough parallel horizontal falls located in a uniform vertical magnetic field region as shown. The cylinder starts rolling without slipping on the rails. The acceleration of the cylinder is

A point electric dipole with a moment p is placed in the external uniform electric field whose strength equals E_(0) . With p uarr uarr E_(0) . In this case one of the equipotential surfaces enclosing the dipole from a sphere. Find the radius of this sphere.

A small ball ( uniform solid sphere ) of mass m is released from the top of a wedge of the same mass m . The wedge is free to move on a smooth horizontal surface. The ball rolld without sliding on the wedge. The required height of the wedge are mentioned in the figure. The speed of the wedge when the ball is just going to leave the wedge at point 'P' of the wedge is

A short electric dipole of dipole moment P is placed in stable equilibrium in uniform electric field E as shown in the figure. The work done by the external agent to rotate the dipole slowly up to its unstable equilibrium will be