Question

Find magnitude and direction of acceleration of center of mass of the system.?

Answer 1

$T-2g=2a$

$5g-T=5a$

$\overline{3g=7a}$

$\Rightarrow a=\frac{3g}{7}$

$\Rightarrow a=\frac{30}{7}m{s}^{-2}$

$a_{cm}=\frac{2\times \left(\frac{30}{7}\right)+5\left(\frac{-30}{7}\right)}{2+5}$

$=\frac{\frac{60}{7}-\frac{150}{7}}{7}=\frac{-\frac{90}{7}}{7}=-\frac{90}{14}$

$\Rightarrow a_{cm}=\frac{45}{7}m{s}^{-2}$