1. Analyze Statement 1

In a completely inelastic collision, the two particles stick together after collision.

Let masses be $m_1, m_2$ and initial velocities be $u_1, u_2$, both in the same direction.

After collision, common velocity is $v$.

By conservation of momentum,

So,

Since both $u_1$ and $u_2$ are in the same direction, $v\neq 0$ (unless both were zero initially, which is not the intended case).

Hence final kinetic energy is

So all kinetic energy is not lost.

Therefore, Statement 1 is true.

2. Analyze Statement 2

The principle of conservation of momentum holds for every collision provided no external force acts on the system.

Thus it is valid for:

• elastic collisions
• inelastic collisions
• completely inelastic collisions

Therefore, Statement 2 is true.

3. Check whether Statement 2 explains Statement 1

Yes. In Statement 1, the reason all energy cannot be lost is that even in a completely inelastic collision, momentum must still be conserved.

If two particles are moving in the same direction initially, the total initial momentum is nonzero:

Therefore after collision the combined body must also have nonzero momentum:

So $v\neq 0$, and therefore the final kinetic energy cannot be zero.

Thus, Statement 2 is the correct explanation of Statement 1.

4. Evaluate options

• A: True, True, and Statement 2 correctly explains Statement 1 ✅
• B: True, True, but not explanation ❌
• C: Statement 1 false, Statement 2 true ❌
• D: Statement 1 true, Statement 2 false ❌

5. Final Answer

The correct option is: