---
title: "Two spheres of identical shape and size, Sphere 1 of mass \\(m\\) and Sphere 2 of mass \\(2m\\), fall vertically through the atmosphere where each experiences a resistive drag force modeled by \\(F_D = bv^2\\), with \\(b\\) being a positive constant. Let \\(v_{T,1}\\) and \\(v_{T,2}\\) represent the terminal speeds of Sphere 1 and Sphere 2, respectively. Both spheres are launched vertically downward with the same initial speed \\(v_0 = v_{T,1}\\). What are the initial acceleration \\(a_0\\) of Sphere 2 immediately after launch and the ratio \\(\\dfrac{v_{T,2}}{v_{T,1}}\\) of their terminal speeds?"
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url: "https://nerd-notes.com/ubq/120559/"
date_modified: "2026-08-23T04:41:38+00:00"
---

# Two spheres of identical shape and size, Sphere 1 of mass \(m\) and Sphere 2 of mass \(2m\), fall vertically through the atmosphere where each experiences a resistive drag force modeled by \(F_D = bv^2\), with \(b\) being a positive constant. Let \(v_{T,1}\) and \(v_{T,2}\) represent the terminal speeds of Sphere 1 and Sphere 2, respectively. Both spheres are launched vertically downward with the same initial speed \(v_0 = v_{T,1}\). What are the initial acceleration \(a_0\) of Sphere 2 immediately after launch and the ratio \(\dfrac{v_{T,2}}{v_{T,1}}\) of their terminal speeds?

Two spheres of identical shape and size, Sphere 1 of mass \(m\) and Sphere 2 of mass \(2m\), fall vertically through the atmosphere where each experiences a resistive drag force modeled by \(F_D = bv^2\), with \(b\) being a positive constant. Let \(v_{T,1}\) and \(v_{T,2}\) represent the terminal speeds of Sphere 1 and Sphere 2, respectively. Both spheres are launched vertically downward with the same initial speed \(v_0 = v_{T,1}\). What are the initial acceleration \(a_0\) of Sphere 2 immediately after launch and the ratio \(\dfrac{v_{T,2}}{v_{T,1}}\) of their terminal speeds?

- **A.** Initial acceleration: \(g\) downward ; Ratio: \(2\)
- **B.** Initial acceleration: \(\dfrac{g}{2}\) downward ; Ratio: \(2\)
- **C.** Initial acceleration: \(g\) downward ; Ratio: \(\sqrt{2}\)
- **D.** Initial acceleration: \(\dfrac{g}{2}\) downward ; Ratio: \(\sqrt{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120559/*