A thin copper plate of mass m has a shape of a square with a side b and thickness d. The plate is suspended on a vertical spring with a force constant k in a uniform horizontal magnetic field B parallel to the plane of the plate. Find the period of the small amplitude vertical oscillations of the plate.

Why a thick metal plate oscillating about a horizontal axis stops when a strong magnetic field is applied on the plane?

Consider the plane of the paper to be vertical plane with direction of 'g' as shown in the figure. A rod (MM') of mass 'M' and carrying a current I . The rod is suspended vertically through two insulated spring of spring constant K at two ends. A uniform magnetic field is applied perpendicular to the plane of the paper such that the potential energy stored in the spring, in equilibrium position is zero. If the rod is slightly displaced in the vertically direction from the position of equilibrium, then the time period of oscillation is

A uniform square plate at side a is hinged at one at its comes it is suspended such than it can rotate about horizontal axis. The time period of small oscillation about its equilibrium position.

A uniform squre plate of mass m is supported in a horizaontal plane by a vertical pin at B and is attached at A to a spring of constant K. If corner A is given a small displacement and released, determine the period of the resulting motion.

The plates each of area A of a parallel plate caoacitor are given charges Q and -Q . The plates are joined by a non-conducting spring of force constant k . The natural length of the spring is d , the inital separation between the plates. The left plate is connected to a vertical wall through a massless non-conducting rope and the right plate is connected to a block of mass m through similar rope. Assume the pulley to be massless, neglect dielectric effect of the spring and Q^(2) lt 2mAepsilon_(0)g If T be the time period of oscillation, then

Figure shows two metallic plates A and B placed parallel to each other at a seperation d. A uniform electric field E exists between the plates in the direction from plate B to plate A. Find the potential difference between the plates.

The plates each of area A of a parallel plate caoacitor are given charges Q and -Q . The plates are joined by a non-conducting spring of force constant k . The natural length of the spring is d , the inital separation between the plates. The left plate is connected to a vertical wall through a massless non-conducting rope and the right plate is connected to a block of mass m through similar rope. Assume the pulley to be massless, neglect dielectric effect of the spring and Q^(2) lt 2mAepsilon_(0)g If Q^(2)=2mAepsilon_(0)g , the elongation of the string is

The plates each of area A of a parallel plate caoacitor are given charges Q and -Q . The plates are joined by a non-conducting spring of force constant k . The natural length of the spring is d , the inital separation between the plates. The left plate is connected to a vertical wall through a massless non-conducting rope and the right plate is connected to a block of mass m through similar rope. Assume the pulley to be massless, neglect dielectric effect of the spring and Q^(2) lt 2mAepsilon_(0)g . If the block is released from rest, the maximum elongation of the string is

A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal the passing through A. If the cable at B breaks then just after that the angular acceleration of the plate is

A square plate of side 'a' and mass 'm' is lying on a horizontal floor. A force F is applied at the top. Find the maximum force that can be applied on the square plate so that the plate does not topple about A.