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.
Text Solution
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Let us assume that `m_(2)gtm_(1)`. We can see that the masses have equal and opposite acceleration of the same magnitude. `a=(m_(2)-m_(1))/(m_(2)+m_(1))g` and tension in string 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)
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CENGAGE PHYSICS ENGLISH-CENTRE OF MASS-INTEGER_TYPE
