By the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.

Before the collision, the momentum is given by:

\(m \times 2 + 0 \times 0.2 = 2m\)

After the collision, the momentum is given by:

\(m \times (-0.5) + 0.2 \times 1 = -0.5m + 0.2\)

Setting the total momentum before and after the collision equal gives:

\(2m = -0.5m + 0.2\)

Solving for \(m\):

\(2m + 0.5m = 0.2\)

\(2.5m = 0.2\)

\(m = \frac{0.2}{2.5} = 0.08\)