A pulley fixed to the ceiling carried a thread with bodies of masses m_(1) and m_(2) attached to its ends. The mases of the pulley and the thread are negligible and friction is absent. Find the acceleration of the centre of mass of this system.

A pulley fixed to the ceiling carried a thread with bodies of masses m

1.	A pulley fixed to the ceiling carried a thread with bodies of masses m_(1) and m_(2) attached to its ends. The mases of the pulley and the thread are negligible and friction is absent. Find the acceleration of the centre of mass of this system.
Answer» SOLUTION :Let US assume that `m_(2)gtm_(1)`. We can see that the masses have equaland opposite acceleration of the same magnitude. `a=(m_(2)-m_(1))/(m_(2)+m_(1))g` and tension instring is `T=(2m_(1)m_(2)g)/(m_(2)+m_(1))` Taking downward direction as positive `a_(1)=-,a_(2)=+a` `a_(CM)=(m_(1)a_(1)+m_(2)a_(2))/(m_(1)+m_(2))=((m_(2)-m_(1))a)/(m_(2)+m_(1))` substituting for the value of a we have `a_(CM)=((m_(2)-m_(1))/(m_(2)+m_(1)))^(2) g` Alternative method: `a_(CM)=F_(ext)/(m_(1)+m_(2))=((m_(1)g+m_(2)g)-2T)/(m_(1)+m_(2))=g-(2T)/(m_(1)+m_(2))` `=g-(4m_(1)m_(2)g)/((m_(2)+m_(1))^(2))=((m_(2)-m_(1))/(m_(2)+m_(1)))^(2)g` (DOWNWARDS)