---
title: "A pulley of mass M and radius R is mounted on a horizontal, frictionless axle. The pulley can be treated as a solid disk with a rotational inertia of I = 1/2 MR^2. A light string is wrapped around the pulley and attached to a block of mass m, which is released from rest and allowed to fall. The string does not slip on the pulley as it unwinds. Which of the following expressions represents the magnitude of the angular acceleration of the pulley as the block falls?"
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url: "https://nerd-notes.com/ubq/111276/"
date_modified: "2026-04-10T01:19:53+00:00"
---

# A pulley of mass M and radius R is mounted on a horizontal, frictionless axle. The pulley can be treated as a solid disk with a rotational inertia of I = 1/2 MR^2. A light string is wrapped around the pulley and attached to a block of mass m, which is released from rest and allowed to fall. The string does not slip on the pulley as it unwinds. Which of the following expressions represents the magnitude of the angular acceleration of the pulley as the block falls?

A pulley of mass M and radius R is mounted on a horizontal, frictionless axle. The pulley can be treated as a solid disk with a rotational inertia of I = 1/2 MR^2. A light string is wrapped around the pulley and attached to a block of mass m, which is released from rest and allowed to fall. The string does not slip on the pulley as it unwinds. Which of the following expressions represents the magnitude of the angular acceleration of the pulley as the block falls?

![A side view diagram showing a circular pulley of radius R and mass M mounted to a wall. A vertical string is wrapped around the pulley's circumference and hangs down. A square block of mass m is attached to the end of the hanging string. An arrow indicates the block is moving downward.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775783992-XBx38a.jpg)

- **A.** \(\dfrac{mg}{R(m + \frac{1}{2}M)}\)
- **B.** \(\dfrac{mg}{R(m + M)}\)
- **C.** \(\dfrac{2mg}{RM}\)
- **D.** \(\dfrac{g}{R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111276/*