---
title: "A ball of mass \\( M \\) is attached to a string of length \\( L \\). It moves in a vertical circle and at the bottom the ball just clears the ground. The tension at the bottom of the path is \\( 3 \\) times the weight of the ball. Give all answers in terms of \\( M \\), \\( L \\), and \\( g \\)."
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url: "https://nerd-notes.com/ubq/21869/"
date_modified: "2025-04-18T03:28:33+00:00"
---

# A ball of mass \( M \) is attached to a string of length \( L \). It moves in a vertical circle and at the bottom the ball just clears the ground. The tension at the bottom of the path is \( 3 \) times the weight of the ball. Give all answers in terms of \( M \), \( L \), and \( g \).

A ball of mass \( M \) is attached to a string of length \( L \). It moves in a vertical circle and at the bottom the ball just clears the ground. The tension at the bottom of the path is \( 3 \) times the weight of the ball. Give all answers in terms of \( M \), \( L \), and \( g \).

**Part a)** What is the magnitude and direction of the net force of the ball when it is at the top? *(3 points)*

**Part b)** What is the velocity of the ball at the top? *(3 points)*

**Part c)** The string is cut exactly when the ball is at the top. How long does it take to reach the ground? *(3 points)*

**Part d)** How far does the ball travel horizontally before hitting the ground? *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/21869/*