Question

Two spheres, \( A \) and \( B \), of identical size and surface material, but different masses, are dropped from rest near the surface of Earth. While falling, each sphere experiences a resistive force which is proportional to the sphere's velocity. What are the relationships of the magnitude of the initial acceleration \( a_{0} \) of each sphere and of the terminal speed \( v_{T} \) of each sphere if \( m_{\mathrm{A}}<m_{\mathrm{B}} \) ? \begin{tabular}{lll} & Initial Acceleration & Terminal Speed \\ \hline A & \( a_{0, \mathrm{~A}}=a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}=v_{T, \mathrm{~B}} \) \\ B & \( a_{0, \mathrm{~A}}=a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}<v_{T, \mathrm{~B}} \) \\ C & \( a_{0, \mathrm{~A}}<a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}=v_{T, \mathrm{~B}} \) \\ D & \( a_{0, \mathrm{~A}}<a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}<v_{T, \mathrm{~B}} \) \end{tabular}

          Two spheres, \( A \) and \( B \), of identical size and surface material, but different masses, are dropped from rest near the surface of Earth. While falling, each sphere experiences a resistive force which is proportional to the sphere's velocity. What are the relationships of the magnitude of the initial acceleration \( a_{0} \) of each sphere and of the terminal speed \( v_{T} \) of each sphere if \( m_{\mathrm{A}}<m_{\mathrm{B}} \) ?
\begin{tabular}{lll} 
& Initial Acceleration & Terminal Speed \\
\hline A & \( a_{0, \mathrm{~A}}=a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}=v_{T, \mathrm{~B}} \) \\
B & \( a_{0, \mathrm{~A}}=a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}<v_{T, \mathrm{~B}} \) \\
C & \( a_{0, \mathrm{~A}}<a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}=v_{T, \mathrm{~B}} \) \\
D & \( a_{0, \mathrm{~A}}<a_{0, \mathrm{~B}} \) & \( v_{T, \mathrm{~A}}<v_{T, \mathrm{~B}} \)
\end{tabular}

Two spheres, A and B, of identical size and surface material, but different masses, are dropped from rest near the surface of Earth. While falling, each sphere experiences a resistive force which is proportional to the sphere's velocity. What are the relationships of the magnitude of the initial acceleration a0 of each sphere and of the terminal speed vT of each sphere if mA<mB ?

Initial Acceleration Terminal Speed

A a0, A=a0, B vT, A=vT, B

B a0, A=a0, B vT, A<vT, B

C a0, A<a0, B vT, A=vT, B

D a0, A<a0, B vT, A<vT, B

Added by Natalie T.

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