**Elastic Collision**

In an elastic collision, both the momentum and kinetic energy are conserved. Momentum is defined as the product of mass and velocity, while kinetic energy is defined as the energy possessed by an object due to its motion.

**Given Information:**
- A heavy body moving with a velocity of 20 m/s
- Another small object at rest

**Velocity of the Small Object After Collision:**

Since the collision is elastic, both momentum and kinetic energy will be conserved.

**Conservation of Momentum:**
The total momentum before the collision is equal to the total momentum after the collision.

Let the mass of the heavy body be M and the mass of the small object be m.

Initial momentum = M * 20 m/s (since the heavy body is moving with a velocity of 20 m/s)
Final momentum = M * V + m * V (where V is the velocity of both objects after the collision)

According to the conservation of momentum:
M * 20 = M * V + m * V

**Conservation of Kinetic Energy:**
The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Initial kinetic energy = 0.5 * M * (20)^2 (since the small object is at rest)
Final kinetic energy = 0.5 * M * V^2 + 0.5 * m * V^2

According to the conservation of kinetic energy:
0.5 * M * (20)^2 = 0.5 * M * V^2 + 0.5 * m * V^2

**Solving the Equations:**

We have two equations from the conservation of momentum and kinetic energy.

Equation 1: M * 20 = M * V + m * V
Equation 2: 0.5 * M * (20)^2 = 0.5 * M * V^2 + 0.5 * m * V^2

By substituting Equation 1 into Equation 2, we can solve for V.

0.5 * M * (20)^2 = 0.5 * M * (M * 20 + m * 20)^2 + 0.5 * m * (M * 20 + m * 20)^2

Simplifying the equation yields:
200M = 220MV + 40mV + 20m^2

Simplifying further gives:
200 = 220V + 40m/M * V + 20m^2/M

Now, we can solve for V.

**Answer:**

The velocity of the small object after the elastic collision is:
V = (200 - 40m/M - 20m^2/M) / (220)

Since we don't have the specific mass values for the objects, we cannot determine the exact velocity. However, we can conclude that the velocity of the small object will not be zero, as the heavy body imparts some of its momentum to the small object during the collision. Therefore, the correct answer is **A) 20 m/s**.