---
title: "A small block of mass \\(0.20\\text{ kg}\\) is initially at rest at the apex of a smooth, frictionless hemispherical dome of radius \\(R = 7.5\\text{ m}\\) fixed to a horizontal floor. The block is given a negligible push and begins to slide down the curved surface. What is the speed of the block at the instant it loses contact with the dome?"
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url: "https://nerd-notes.com/ubq/120677/"
date_modified: "2026-08-23T04:42:38+00:00"
---

# A small block of mass \(0.20\text{ kg}\) is initially at rest at the apex of a smooth, frictionless hemispherical dome of radius \(R = 7.5\text{ m}\) fixed to a horizontal floor. The block is given a negligible push and begins to slide down the curved surface. What is the speed of the block at the instant it loses contact with the dome?

A small block of mass \(0.20\text{ kg}\) is initially at rest at the apex of a smooth, frictionless hemispherical dome of radius \(R = 7.5\text{ m}\) fixed to a horizontal floor. The block is given a negligible push and begins to slide down the curved surface. What is the speed of the block at the instant it loses contact with the dome?

![A grayscale side-view schematic showing a semicircular dome of radius \(R\) resting flat on a horizontal ground line. A small rectangular block sits on the curved upper surface of the dome at an angle \(\theta\) measured clockwise from the vertical dashed centerline passing through the dome's apex and center. A radial dashed line connects the center of the dome to the block. An arrow labeled \(v\) points tangentially downward along the curve from the block. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460158-pDvaRM.jpg)

- **A.** \(6.1\text{ m/s}\)
- **B.** \(7.0\text{ m/s}\)
- **C.** \(8.6\text{ m/s}\)
- **D.** \(12\text{ m/s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120677/*