Two masses m 1 and m 2 (m 1 > m 2 ) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of center of mass is
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Acceleration of each mass \(a = \left(\frac{m_1 - m_2}{m_1 + m_2}\right) g\)
Now acceleration of center of mass of the system
\(\vec{A}_{cm} = \frac{m_1 \vec{a}_1 + m_2 \vec{a}_2}{m_1 + m_2}\)
As both masses move with same acceleration but in opposite direction so \vec{a}_1 = - \vec{a}_2 = a (let)
\(\therefore \; A_{cm} = \frac{m_1 a - m_2 a}{m_1 + m_2}\)
\(= \left(\frac{m_1 - m_2}{m_1 + m_2}\right) \times \left(\frac{m_1 - m_2}{m_1 + m_2}\right) \times g\)
\(= \left(\frac{m_1 - m_2}{m_1 + m_2}\right)^2 \times g^-\)
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