What is the Dipole moments of para di hydroxy benzene

TheOatom is sp3hybridized, thus C-O-Hbond angle would be about 109°.

With free rotation about theC-Obond, the opposingO-Hbond dipoles would still cancel each other.

The dipole moment would be zero.

It appears that theOatoms aresp2hybridized for resonance with the benzene ring.
This prevents free rotation about theC-Obonds and gives rise tocisandtrans isomers.
Thecisisomer has theO-Hbonds pointing to the same side of the ring.
TheO-Hdipole moments (red) reinforce each other to give a resultant molecular dipole (blue).
Thetransisomer has theO-Hbonds pointing to opposite sides of the ring.
It may look as if theO-Hdipole moments (red) do not cancel each other.
However, if we slide them to put their origins in the centre of the ring (blue), we see that they are pointing in exactly opposite directions.
The bond dipoles cancel, so the predicted molecular dipole moment isµ=0.

The observed dipole moment of benzene-1,4-diol is 1.4 D.

It appears that the observed dipole moment is a weighted average of the dipole moments of the two conformations.
Cis isomer
Trans isomer