Two masses m_1 and m_2 (m_1 m_2) are connec | vedclass

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(A) The magnitude of acceleration of each mass in an Atwood machine is given by $a = \left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)g$.Let th

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${\left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)^2}g$

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(A) The magnitude of acceleration of each mass in an Atwood machine is given by $a = \left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} ight)g$.Let the downward direction be positive for $m_1$ and upward for $m_2$. Then the acceleration vectors are $\vec{a_1} = a \hat{j}$ and $\vec{a_2} = -a \hat{j}$.The acceleration of the center of mass $(A_{cm})$ is given by:$A_{cm} = \frac{m_1 \vec{a_1} + m_2 \vec{a_2}}{m_1 + m_2}$$A_{cm} = \frac{m_1 (a) - m_2 (a)}{m_1 + m_2} = \left( \frac{m_1 - m_2}{m_1 + m_2} ight) a$Substituting the value of $a$:$A_{cm} = \left( \frac{m_1 - m_2}{m_1 + m_2} ight) 	imes \left( \frac{m_1 - m_2}{m_1 + m_2} ight) g$$A_{cm} = {\left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} ight)^2}g$

Two masses $m_1$ and $m_2$ $(m_1 > m_2)$ are connected by a massless,flexible,and inextensible string passed over a massless and frictionless pulley. The acceleration of the center of mass of the system is

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