Solution:

Given, a wire of resistance R is connected to a potential difference V.
We need to find the effect on the drift velocity of electrons when the wire is stretched to double its length while keeping the potential difference same.

Effect on resistance:
When a wire is stretched, its length increases and therefore its resistance also increases.

Resistance of wire, R = ρL/A
where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

Now, when the length of the wire is doubled, its resistance becomes:
R' = ρ(2L)/A
R' = 2ρL/A
R' = 2R (since L and A are constant)

Hence, the resistance of the wire becomes twice its original value when it is stretched to double its length while keeping the potential difference same.

Effect on current:
According to Ohm's law, V = IR, where V is the potential difference, I is the current, and R is the resistance of the wire.

When the resistance of the wire is doubled, the current flowing through it becomes half because of the same potential difference across the wire. (V = IR)

Effect on drift velocity of electrons:
The current flowing through a wire is given by I = neAvd
where n is the number of free electrons per unit volume, e is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity of electrons.

Since the potential difference and the number of free electrons per unit volume remain constant, the drift velocity of electrons is directly proportional to the current flowing through the wire.

Therefore, when the current becomes half, the drift velocity of electrons also becomes half.

Answer:
Hence, the correct option is (3) Become half.