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(C) The formula $a = \frac{(m_1 - m_2)g}{m_1 + m_2}$ is derived for an Atwood machine.To derive this,we assume:$1$. The string is massless,which ensur

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pulley is massless

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(C) The formula $a = \frac{(m_1 - m_2)g}{m_1 + m_2}$ is derived for an Atwood machine.To derive this,we assume:$1$. The string is massless,which ensures that the tension $T$ is uniform throughout the string.$2$. The string is inextensible,which ensures that both masses have the same magnitude of acceleration.$3$. The pulley is frictionless,which ensures that the tension remains the same on both sides of the pulley.$4$. The pulley is assumed to be massless to ignore its moment of inertia. However,if the pulley has mass,it would require a torque to rotate,which would change the tension on either side. But in the standard derivation of this specific formula,the pulley is treated as an ideal point of redirection. Among the given options,the assumption that the pulley is massless is not strictly required to derive the acceleration formula if we only consider the translational motion of the blocks and assume the pulley is just a simple redirection point,whereas the other three are fundamental to the standard derivation.

$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?

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