---
title: "A block of mass \\(M\\) is placed on a horizontal surface where the coefficient of kinetic friction between the block and the surface is \\(\\mu\\). The block is connected by an ideal string over a light, frictionless pulley to a hanging block of mass \\(m\\). When the system is released from rest, the blocks move with a constant acceleration of magnitude \\(a\\). The hanging block is then replaced with a new block of mass \\(2m\\), and the system is again released from rest. If the blocks still accelerate, which of the following expressions correctly represents the magnitude of the new acceleration \\(a’\\) in terms of \\(a\\), \\(M\\), \\(m\\), and \\(g\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/109271/"
date_modified: "2026-03-21T18:52:40+00:00"
---

# A block of mass \(M\) is placed on a horizontal surface where the coefficient of kinetic friction between the block and the surface is \(\mu\). The block is connected by an ideal string over a light, frictionless pulley to a hanging block of mass \(m\). When the system is released from rest, the blocks move with a constant acceleration of magnitude \(a\). The hanging block is then replaced with a new block of mass \(2m\), and the system is again released from rest. If the blocks still accelerate, which of the following expressions correctly represents the magnitude of the new acceleration \(a’\) in terms of \(a\), \(M\), \(m\), and \(g\)?

A block of mass \(M\) is placed on a horizontal surface where the coefficient of kinetic friction between the block and the surface is \(\mu\). The block is connected by an ideal string over a light, frictionless pulley to a hanging block of mass \(m\). When the system is released from rest, the blocks move with a constant acceleration of magnitude \(a\). The hanging block is then replaced with a new block of mass \(2m\), and the system is again released from rest. If the blocks still accelerate, which of the following expressions correctly represents the magnitude of the new acceleration \(a'\) in terms of \(a\), \(M\), \(m\), and \(g\)?

![A block of mass M sits on a horizontal table. A string is attached to its right side, passing over a pulley at the edge of the table. A block of mass m is hanging vertically from the string. The table surface is labeled with a coefficient of friction mu.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774119160-2uc4W1.jpg)

- **A.** \(a' = 2a\)
- **B.** \(a' = \dfrac{2a(M+m)}{M+2m}\)
- **C.** \(a' = \dfrac{mg + a(M+m)}{M+2m}\)
- **D.** \(a' = \dfrac{mg - a(M+m)}{M+2m}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109271/*