Consider the situation shown in figure .The plates of the capacitor have plate area `A` and are clapmed in the laborstory . The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that slab will execute periodie motion and find its time period.

For a capacitor the distane between two plates is 4x and the electric field between them is E_(0) . Now a dielectric slab having dielectric constant 3 and thickkness x is placed between them in contact with one plate. In this condition what is the p.d. between its two plates ?

The capacitance of a parallel capacitor is 5 mu F. When glass slab inserting between two plates, its potential difference becomes (1)/(8) the times hence the dielectric constant of a slab ......

A cylinderical rod of length l=2m & density (rho)/(2) floats vertically in a liquid of density rho as shown in figure (i). Show that it performs SHM when pulled slightly up & released find its time period. Neglect change in liquid level. (ii). Find the time taken by the rod to completely immerse when released from position shown in (b). Assume that it remains vertical throughout its motion (take g=pi^(2)m//s^(2) )

In the diagram shown below, the rod is uniform having mas M and length L. When it is making an angle = 60^(@) the rod is released from the state of rest (and spring in its natural lenth) The rod comes to state of rest when the angle theta reduces to 30^(@) . What should be the initial compression in the spring (when theta = 60^(@)) so that the whole system can remain in the state of rest? (there is no friction between any surfaces)

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d_(1) and dielectric constant k_(1) and the other has thickness d_(2) and dielectric constant k_(2) as shown in figure. This arrangement can be thought as a dielectric slab of thickness d = ( d_(1) + d_(2) ) and effective dielectric constant k. The k is ...... (a) (K_(1)d_(1)+K_(2)d_(2))/(d_(1)+d_(2)) (b) (K_(1)d_(1)+K_(2)d_(2))/(K_(1)+K_(2)) (c) (K_(1)K_(2)(d_(1)+d_(2)))/((K_(1)d_(2)+K_(2)d_(1))) (d) (2K_(1)K_(2))/(K_(1)+K_(2))