Two point masses of mass m and equal and opposite charge of magnitude q are attached on the corners of a non-conducting uniform rod of mass m and the system is released from rest in uniform electric field E as shown in figure from `theta=53^(@)`

(i) Find angular acceleration of the rod just after releasing
(ii) What will be angular velocity of the rod when it passes through stable equilibrium.
(iii) Find work required to rotate the system by `180^(@)`.

Explanation

(i) `tau_("net")=PE sin 53^(@)= I alpha`
`:. alpha=((ql) E (4/5))/((ml^(2))/12+m(l/2)^(2)+m(l/2)^(2))=(48qE)/(35 ml)`
(ii) From energy conservation : `K_(i)+U_(i)=K_(f)+U_(f)`
`:. 0+(-PE cos 53^(@))=1/2 Iomega^(2)+(-PE cos 0^(@))`
where `I=(ml^(2))/12+m (l/2)^(2)+m(l/2)^(2)=(7ml^(2))/12" ":." "1/2 Iomega^(2)=PE (1-3//5)=2/5 PE`
`:. 1/2xx(7 m l^(2))/12xxomega^(2) =2/5" "qlE` or `omega=sqrt((48 qE)/(35 ml))`
(iii) `:' W_("ext")=U_(f)-U_(i)`
`:. W_("ext")=(-PE cos (180^(@)+53^(@)))-(-PE cos 53^(@))`
or `W_("ext")=(ql)E(3/5)+(ql)E(3/5)" "implies" "W_("ext")=(6/5) qlE`