Question

A uniform beam of length `L`. And mass `m` is supported as shown. Of the cable suddenly breaks, determine ,
(a) the acceleration of end `B`.
(b) the reaction at the pin support.
.

Answer 1

Correct Answer - (a) `(9g)/(7)darr`
(b) `(4 mg)/(7)uarr`
(a) As the string breaks torque about `O`

`mg xx (L)/(4) = I alpha`
`mg (L)/(4) = [(1)/(12) mL^(2) +m((L)/(4))^(2)] alpha`
`alpha = (12g)/(7 L)`
The angular acceleration of rod is `alpha = (12 g)/(7 L)`
`a_(B) = ((3L)/(4)) xx alpha rArr a_(B) = (3L)/(4) xx (12 g)/(7L)`
`a_(B) = (9g)/(7) m//s^(2) darr`
(b) Let the reaction at pint support be `R`.
by force equation
`mg - R = ma_(cm) rArr mg - ma_(cm) = R`
`a_(cm) = (L)/(4) alpha rArr a_(cm) = (3g)/(7)`
`mg - m xx (3g)/(7) = R rArr R = (4mg)/(7) uarr`.