---
title: "A block of mass \\(m\\) is placed on the smooth inclined face of a wedge of mass \\(M\\), which makes an angle \\(\\theta\\) with the horizontal. The wedge rests on a frictionless horizontal floor. The block is released from rest, and all contact surfaces are frictionless. Which of the following expressions gives the magnitude of the horizontal acceleration of the wedge as the block slides down the incline?"
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url: "https://nerd-notes.com/ubq/124243/"
date_modified: "2026-09-28T14:04:28+00:00"
---

# A block of mass \(m\) is placed on the smooth inclined face of a wedge of mass \(M\), which makes an angle \(\theta\) with the horizontal. The wedge rests on a frictionless horizontal floor. The block is released from rest, and all contact surfaces are frictionless. Which of the following expressions gives the magnitude of the horizontal acceleration of the wedge as the block slides down the incline?

A block of mass \(m\) is placed on the smooth inclined face of a wedge of mass \(M\), which makes an angle \(\theta\) with the horizontal. The wedge rests on a frictionless horizontal floor. The block is released from rest, and all contact surfaces are frictionless. Which of the following expressions gives the magnitude of the horizontal acceleration of the wedge as the block slides down the incline?

![A schematic side-view diagram showing a right-triangular wedge resting on a horizontal floor. The floor is represented by a single straight horizontal baseline. The wedge has mass label \(M\) positioned within its triangular boundary, a horizontal bottom edge flush against the floor, a vertical edge on the left, and an inclined face that slopes downward to the right. An arc at the lower-right corner between the inclined face and the horizontal floor is labeled \(\theta\). A small rectangular block with mass label \(m\) inside it sits on the inclined face midway along the slope. No arrows, components, motion indicators, coordinate axes, or additional labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604267-ORygcI.jpg)

- **A.** \(\dfrac{mg \sin\theta \cos\theta}{M}\)
- **B.** \(\dfrac{mg \sin\theta \cos\theta}{M + m}\)
- **C.** \(\dfrac{mg \sin\theta \cos\theta}{M + m \sin^2\theta}\)
- **D.** \(\dfrac{mg \sin\theta \cos\theta}{M + m \cos^2\theta}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124243/*