The capacitor plates are fixed on an inclined plane and connected to a battery of emf E. The capacitor plates have plate area a, length l, and the distance between them is d. A dielectric slab of mass m and dielectric constant K is inserted into the capacitor and tied to mass M by a massless string as shown in the figure. Find the value of M for which the slab will stay in equilibrium. There is no friction between slab and plates. 

• A

  $\frac{\mathrm{m}}{2}+\frac{{\mathrm{E}}^2{\mathrm{\epsilon }}_0\mathrm{A}(\mathrm{k}-1)}{2\lg \mathrm{d}}$

• B

  $\frac{\mathrm{m}}{2}-\frac{{\mathrm{E}}^2{\mathrm{\epsilon }}_0\mathrm{A}(\mathrm{k}-1)}{2\lg \mathrm{d}}$

• C

  $\frac{\mathrm{m}}{2}+\frac{{\mathrm{E}}^2{\mathrm{\epsilon }}_0\mathrm{A}(\mathrm{k}-1)}{\lg \mathrm{d}}$

• D

  $\frac{\mathrm{m}}{2}-\frac{{\mathrm{E}}^2{\mathrm{\epsilon }}_0\mathrm{A}(\mathrm{k}-1)}{\lg \mathrm{d}}$