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A point particle of mass M is attached to one end of a massless rigid non-conducting rod of length L. Another point particle of the same mass is attached to the other end of the rod. The two particle carry charges + q and – q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle $\mathrm{\theta }$ (say of about 5°) with the field direction (see figure). The expression for the minimum time needed for the rod to become parallel to the field after it is set free.

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Three electric dipoles $\overrightarrow{{\mathrm{p}}_1}, \overrightarrow{{\mathrm{p}}_2 } \mathrm{and} \overrightarrow{{\mathrm{p}}_3}$ are placed along three sides of on equilateral triangle ABC as shown in figure If $\left|\overrightarrow{{\mathrm{p}}_1}\right|= \left|\overrightarrow{{\mathrm{p}}_2 }\right| = \left|\overrightarrow{{\mathrm{p}}_3}\right|=\mathrm{p}$and the dipole $\left|\overrightarrow{{\mathrm{p}}_3}\right|$ is removed from the system, then the resultant dipole moment of the system will be

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