Topic: System of Masses
Concepts: 1D inelastic collision, Conservation of energy, Vertical spring

---

Solution:

Conserving energy for $m_1$, we have

so $m_1$ hits $m_2$ with velocity $v_1=\sqrt{2gh}$. Conserving momentum for the perfectly inelastic collision,

so both masses move with velocity

after the collision.

To find the maximum displacement $x$ of $m_2$ from its original location, we conserve energy again:

so

Note that we can treat the vertical spring as a horizontal spring with a shifted equilibrium so the gravitational potential energy of $m_2$ is already accounted for. Substituting in the given values,

Using the quadratic equation, we find

Hence,

so the answer is B.