---
title: "A spherical balloon of mass \\( 226 \\) \\( \\text{kg} \\) is filled with helium gas until its volume is \\( 325 \\) \\( \\text{m}^3 \\). Assume the density of air is \\( 1.29 \\) \\( \\text{kg/m}^3 \\) and the density of helium is \\( 0.179 \\) \\( \\text{kg/m}^3 \\)."
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url: "https://nerd-notes.com/ubq/87421/"
date_modified: "2025-11-04T18:15:16+00:00"
---

# A spherical balloon of mass \( 226 \) \( \text{kg} \) is filled with helium gas until its volume is \( 325 \) \( \text{m}^3 \). Assume the density of air is \( 1.29 \) \( \text{kg/m}^3 \) and the density of helium is \( 0.179 \) \( \text{kg/m}^3 \).

A spherical balloon of mass \( 226 \) \( \text{kg} \) is filled with helium gas until its volume is \( 325 \) \( \text{m}^3 \). Assume the density of air is \( 1.29 \) \( \text{kg/m}^3 \) and the density of helium is \( 0.179 \) \( \text{kg/m}^3 \).

**Part a)** If the balloon is held to the ground by a vertically oriented string, what is the tension in the string? *(3 points)*

**Part b)** If the string is cut, and a \( 95.5 \)-\( \text{kg} \) basket is now supported beneath the balloon, what is the magnitude and direction of the balloon’s vertical acceleration? *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/87421/*