A uniform rod of mass `m` and length `l` is held horizontally by two vertical strings of negligible mass, as shown in the figure.
(a). Immediately after the right string is cut, what is the linear acceleration of the end of the rod?
(b). Of the middle of the rod?
(c). Determine the tension in the left string immediately after the right string is cut.

Explanation

`alpha=(tau)/(I)=(mg((l)/(2)))/((ml^(2))/(3))=(3)/(2)(g)/(l)`
(a). `a_(B)=lalpha=(3g)/(2)`
(b). `a_(C)=(l)/(2)alpha=(3g)/(4)`
(c). `a_(C)=(mg-T)/(m)` or `(3g)/(4)=(mg-T)/(m)`
`thereforeT=(mg)/(4)`