An insulating long light rod of length L pivoted at its centre O and balanced with a weight W at a distance X from the left end as shown in figure. Charges q and 2q are fixed to the ends of the rod. Exactly below each of these charges at a distance h a positive charge Q is fixed. Then x is

 

• A

  $\frac{\mathrm{QLq} +{{\mathrm{\epsilon }}_0}^2{\mathrm{h}}^2\mathrm{Lw}}{{\mathrm{h}}^2\mathrm{W}}$

• B

  $\frac{\mathrm{QLq}+{\mathrm{\epsilon }}_0{\mathrm{h}}^2\mathrm{LW}}{{\mathrm{\epsilon }}_0{\mathrm{h}}^2\mathrm{W}}$

• C

  $\frac{4\mathrm{QLq}+{\mathrm{\epsilon }}_0{\mathrm{h}}^2\mathrm{LW}}{8{\mathrm{\pi h}}^2\mathrm{W}}$

• D

  $\frac{\mathrm{QLq}+4{\mathrm{\pi \epsilon }}_0{\mathrm{h}}^2\mathrm{LW}}{8{\mathrm{\pi \epsilon }}_0{\mathrm{h}}^2\mathrm{W}}$