---
title: "A cylindrical tank of radius \\(R\\) contains fluid of total mass \\(M\\) distributed uniformly throughout its volume. The fluid swirls about the vertical central axis of the tank such that the tangential speed of a fluid element at a distance \\(r\\) from the axis is given by \\(v(r) = C r^2\\), where \\(C\\) is a positive constant. What is the magnitude of the total angular momentum of the fluid about the central axis?"
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url: "https://nerd-notes.com/ubq/117606/"
date_modified: "2026-08-04T07:49:17+00:00"
---

# A cylindrical tank of radius \(R\) contains fluid of total mass \(M\) distributed uniformly throughout its volume. The fluid swirls about the vertical central axis of the tank such that the tangential speed of a fluid element at a distance \(r\) from the axis is given by \(v(r) = C r^2\), where \(C\) is a positive constant. What is the magnitude of the total angular momentum of the fluid about the central axis?

A cylindrical tank of radius \(R\) contains fluid of total mass \(M\) distributed uniformly throughout its volume. The fluid swirls about the vertical central axis of the tank such that the tangential speed of a fluid element at a distance \(r\) from the axis is given by \(v(r) = C r^2\), where \(C\) is a positive constant. What is the magnitude of the total angular momentum of the fluid about the central axis?

- **A.** \(\dfrac{2}{5} M C R^3\)
- **B.** \(\dfrac{1}{2} M C R^3\)
- **C.** \(\dfrac{1}{3} M C R^3\)
- **D.** \(\dfrac{1}{5} M C R^3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117606/*