---
title: "Three isolated systems, each consisting of two blocks at rest on a frictionless horizontal surface, have the same total mass \\(M\\). An internal explosive mechanism is detonated between the two blocks in each system, delivering an identical impulse of magnitude \\(J_0\\) to each block. The mass distributions of the systems are:  | System | Block 1 Mass | Block 2 Mass | | :— | :— | :— | | 1 | \\(\\dfrac{1}{6}M\\) | \\(\\dfrac{5}{6}M\\) | | 2 | \\(\\dfrac{1}{3}M\\) | \\(\\dfrac{2}{3}M\\) | | 3 | \\(\\dfrac{1}{2}M\\) | \\(\\dfrac{1}{2}M\\) |  Which of the following correctly ranks the total kinetic energy \\(K\\) of the systems immediately after separation?"
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url: "https://nerd-notes.com/ubq/120760/"
date_modified: "2026-08-23T04:43:02+00:00"
---

# Three isolated systems, each consisting of two blocks at rest on a frictionless horizontal surface, have the same total mass \(M\). An internal explosive mechanism is detonated between the two blocks in each system, delivering an identical impulse of magnitude \(J_0\) to each block. The mass distributions of the systems are:

| System | Block 1 Mass | Block 2 Mass |
| :— | :— | :— |
| 1 | \(\dfrac{1}{6}M\) | \(\dfrac{5}{6}M\) |
| 2 | \(\dfrac{1}{3}M\) | \(\dfrac{2}{3}M\) |
| 3 | \(\dfrac{1}{2}M\) | \(\dfrac{1}{2}M\) |

Which of the following correctly ranks the total kinetic energy \(K\) of the systems immediately after separation?

Three isolated systems, each consisting of two blocks at rest on a frictionless horizontal surface, have the same total mass \(M\). An internal explosive mechanism is detonated between the two blocks in each system, delivering an identical impulse of magnitude \(J_0\) to each block. The mass distributions of the systems are:

| System | Block 1 Mass | Block 2 Mass |
| :--- | :--- | :--- |
| 1 | \(\dfrac{1}{6}M\) | \(\dfrac{5}{6}M\) |
| 2 | \(\dfrac{1}{3}M\) | \(\dfrac{2}{3}M\) |
| 3 | \(\dfrac{1}{2}M\) | \(\dfrac{1}{2}M\) |

Which of the following correctly ranks the total kinetic energy \(K\) of the systems immediately after separation?

![Three horizontal rows arranged vertically, labeled from top to bottom as System 1, System 2, and System 3. In each row, two rectangular blocks rest on a horizontal baseline. In System 1, the left rectangle has width 0.5 units labeled \frac{1}{6}M and the right rectangle has width 2.5 units labeled \frac{5}{6}M, with a small starburst symbol between them. In System 2, the left rectangle has width 1.0 unit labeled \frac{1}{3}M and the right rectangle has width 2.0 units labeled \frac{2}{3}M, with a small starburst between them. In System 3, both rectangles have equal width 1.5 units, each labeled \frac{1}{2}M, with a small starburst between them. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460182-FaypNh.jpg)

- **A.** \(K_1 = K_2 = K_3\)
- **B.** \(K_3 > K_2 > K_1\)
- **C.** \(K_2 > K_1 > K_3\)
- **D.** \(K_1 > K_2 > K_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120760/*