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
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
${\left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)^2}g$
$\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}g$
$\frac{{{m_1} + {m_2}}}{{{m_1} - {m_2}}}g$
Zero
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
Acceleration of each mass $ = a = \left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)\;g$
Now acceleration of centre of mass of the system
${A_{cm}} = \frac{{{m_1}\overrightarrow {{a_1}} + {m_1}\overrightarrow {{a_2}} }}{{{m_1} + {m_2}}}$
As both masses move with same acceleration but in opposite direction so
$\overrightarrow {{a_1}} = - \overrightarrow {{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$