1. **Problem Statement:** Two particles P and Q with masses 4 kg and 7 kg are moving towards each other along the same straight line with speeds 10 m/s each. After collision, they move as a single body. Find the speed of the combined particle after the collision. 2. **Formula Used:** We use the law of conservation of linear momentum for perfectly inelastic collision (since they move as a single body after collision): $$m_1 u_1 + m_2 u_2 = (m_1 + m_2) v$$ where $m_1, m_2$ are masses, $u_1, u_2$ are initial velocities, and $v$ is the final velocity of the combined mass. 3. **Important Note:** Since particles move towards each other, assign one velocity as positive and the other as negative to indicate opposite directions. Let P's velocity be positive and Q's velocity negative. 4. **Substitute values:** $$4 \times 10 + 7 \times (-10) = (4 + 7) v$$ $$40 - 70 = 11 v$$ $$-30 = 11 v$$ 5. **Solve for $v$:** $$v = \frac{-30}{11} = -2.727 \text{ m/s}$$ 6. **Interpretation:** The negative sign indicates the combined particle moves in the direction of Q's initial velocity (opposite to P's initial direction) with speed approximately 2.73 m/s. **Final answer:** The speed of the combined particle after collision is approximately $2.73$ m/s in the direction of Q's initial motion.