Given:
Initial velocity (u) = ?
Final velocity (v) = 0
Distance penetrated (s) = 3 cm
Additional distance penetrated (x) = ?

Approach:
To solve this problem, we can use the concept of conservation of mechanical energy. When an object penetrates a wooden block, its initial kinetic energy is converted into potential energy and work done against friction.

We can write the equation for conservation of mechanical energy as:
Initial kinetic energy (KE) = Final potential energy (PE) + Work done against friction

Step 1: Finding the initial velocity (u)
Since the initial velocity is not given, we need to find it using the given information.
We know that the body loses half of its velocity on penetrating 3 cm in the wooden block. This means when it penetrates 3 cm, its velocity becomes half of the initial velocity.

Let's assume the initial velocity (u) = V
After penetrating 3 cm, the velocity becomes V/2.

Using the equation for uniformly accelerated motion:
v^2 = u^2 - 2as

Substituting the values:
(0)^2 = (V/2)^2 - 2(1)(3)
0 = (V^2/4) - 6
V^2/4 = 6
V^2 = 24
V = √24
V = 2√6 cm/s

Therefore, the initial velocity (u) is 2√6 cm/s.

Step 2: Finding the additional distance penetrated (x)
Now that we know the initial velocity (u) and the final velocity (v), we can find the additional distance penetrated (x) before the body comes to rest.

Using the equation for uniformly accelerated motion:
v^2 = u^2 - 2as

Substituting the values:
(0)^2 = (2√6)^2 - 2(1)(x + 3)
0 = 24 - 2(x + 3)
2(x + 3) = 24
x + 3 = 12
x = 9

Therefore, the additional distance penetrated (x) before the body comes to rest is 9 cm.

Conclusion:
The body will penetrate an additional distance of 9 cm before coming to rest. Therefore, the correct option is (d) 4 cm.