The correct option is A 2 cm
Let the electric field at point O due to dipole (1) be E1 and due to dipole (2) be E2.
At O,
E1−E2=0⇒E1=E2
Let point O be x distance away from dipole (1). Then it will be (8−x) distance away from dipole (2)
For a short dipole, electric field at axial line of dipole is given by
|→E|=2k|→p|x3
for electric dipole (1),
E1=2kPx3
and for electric dipole (2),
E2=2k×27P(8−x)3
Since, E1=E2
⇒2kPx3=2k×27P(8−x)3
⇒1x3=27(8−x)3
⇒(8−x)3=33×x3
⇒8−x=3x
⇒x=2 cm
So, option (a) is correct.