---
title: "A block A of mass M on a frictionless horizontal table is connected to a hanging block B of mass M by an ideal, massless cord and ideal pulleys. In Scenario 1, the cord has one end fixed to the ceiling, loops under a light movable pulley from which block B is suspended, passes over a fixed pulley at the edge of the table, and connects directly to block A. In Scenario 2, block B hangs directly from the end of the cord, which passes over the fixed pulley, loops around a light movable pulley attached to block A, and terminates at a fixed anchor near the edge of the table. After both systems are released from rest, what is the ratio of the downward acceleration of block B in Scenario 2 to that in Scenario 1, \\(\\dfrac{a_{B,2}}{a_{B,1}}\\)?"
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url: "https://nerd-notes.com/ubq/124144/"
date_modified: "2026-09-28T13:30:44+00:00"
---

# A block A of mass M on a frictionless horizontal table is connected to a hanging block B of mass M by an ideal, massless cord and ideal pulleys. In Scenario 1, the cord has one end fixed to the ceiling, loops under a light movable pulley from which block B is suspended, passes over a fixed pulley at the edge of the table, and connects directly to block A. In Scenario 2, block B hangs directly from the end of the cord, which passes over the fixed pulley, loops around a light movable pulley attached to block A, and terminates at a fixed anchor near the edge of the table. After both systems are released from rest, what is the ratio of the downward acceleration of block B in Scenario 2 to that in Scenario 1, \(\dfrac{a_{B,2}}{a_{B,1}}\)?

A block A of mass M on a frictionless horizontal table is connected to a hanging block B of mass M by an ideal, massless cord and ideal pulleys. In Scenario 1, the cord has one end fixed to the ceiling, loops under a light movable pulley from which block B is suspended, passes over a fixed pulley at the edge of the table, and connects directly to block A. In Scenario 2, block B hangs directly from the end of the cord, which passes over the fixed pulley, loops around a light movable pulley attached to block A, and terminates at a fixed anchor near the edge of the table. After both systems are released from rest, what is the ratio of the downward acceleration of block B in Scenario 2 to that in Scenario 1, \(\dfrac{a_{B,2}}{a_{B,1}}\)?

![Two schematic diagrams side by side labeled Scenario 1 on the left and Scenario 2 on the right. In Scenario 1, a horizontal surface supports a square labeled A of mass M. A horizontal line extends rightward from block A to the top of a circular fixed pulley at the edge of the surface. A line goes vertically down from the fixed pulley, wraps around the bottom of a circular movable pulley supporting a suspended square labeled B of mass M, and extends vertically upward to a horizontal hatched ceiling. In Scenario 2, the horizontal surface supports a square labeled A of mass M with a small circular movable pulley attached to its right side. Two parallel horizontal lines extend rightward from block A: the lower line attaches to a vertical post at the table edge, and the upper line wraps around the pulley on block A and passes over the fixed pulley at the edge, extending vertically downward to a suspended square labeled B of mass M. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602244-BvxF6J.jpg)

- **A.** \(1\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124144/*