A block `A` of mass `M` kept on a rough horizontal surface is connected to a dielectric slab of mass `M//6` and dielectric constant `k` by means of a light and inextensible string passing over a fixed pulley as shown in the figure. The dielectric can completely fill the space between the parallel plate capacitor of plate area `l xx l` and separation between the plates `d` kept in vertical position. Initially switch `S` is open and length of the dielectric inside the capacitor is `b`. The coefficient of friction between the block `A` and the surface is `mu=1//4`. Igonore any other friction. (Given `(Mgd)/(epsilon_(0)l(k-1))=24`.)
Find the minimum value of the emf `= V` of the battery so that after closing the switch the block `A` will move.

Explanation

`(a) F_(e)+mg ge mumg`
`F_(e) ge (M)/(4)-(M)/(6)g`
`(1)/(2)(epsilon_(0)l)/(d)(k-1)V^(2) ge (Mg)/(12)`
`:. V_(min)=sqrt((Mg)/(12)xx(2d)/(epsilon_(0)l(k-1)))=sqrt((Mgd)/(6epsilon_(0)l(k-1)))`