---
title: "A small solid sphere of mass \\(m\\) is released from rest at time \\(t = 0\\) in a deep tank filled with a viscous fluid. As the sphere falls, the fluid exerts a resistive drag force on the sphere of magnitude \\(F_D = bv\\), where \\(b\\) is a positive constant and \\(v\\) is the downward speed of the sphere. The buoyant force exerted by the fluid on the sphere is negligible."
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url: "https://nerd-notes.com/ubq/117782/"
date_modified: "2026-08-04T07:56:45+00:00"
---

# A small solid sphere of mass \(m\) is released from rest at time \(t = 0\) in a deep tank filled with a viscous fluid. As the sphere falls, the fluid exerts a resistive drag force on the sphere of magnitude \(F_D = bv\), where \(b\) is a positive constant and \(v\) is the downward speed of the sphere. The buoyant force exerted by the fluid on the sphere is negligible.

A small solid sphere of mass \(m\) is released from rest at time \(t = 0\) in a deep tank filled with a viscous fluid. As the sphere falls, the fluid exerts a resistive drag force on the sphere of magnitude \(F_D = bv\), where \(b\) is a positive constant and \(v\) is the downward speed of the sphere. The buoyant force exerted by the fluid on the sphere is negligible.

![A tall vertical rectangular container representing a tank filled with fluid. A horizontal line marks the fluid surface near the top of the container. A small solid circle representing a sphere is located inside the fluid, below the surface line. A vertical downward arrow originates from the center of the sphere, labeled with a lowercase v vector symbol. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830204-bn4ikT.jpg)

**Part a)** A second sphere, identical in size and shape to the first sphere but with mass \(2m\), is released from rest in the same fluid. **Indicate** whether the terminal speed of the second sphere is greater than, less than, or equal to the terminal speed of the first sphere. - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer using qualitative physical reasoning, without referring to an equation.

**Part b)** The following parts refer to the original sphere of mass \(m\). Let the downward direction be positive.

**Part c)** Consider the kinematics and dynamics of the original sphere of mass \(m\) as it falls.


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117782/*