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A uniform beam of length L. And mass m i...

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.
.

Text Solution

Verified by Experts

The correct Answer is:
`(a)(9g)/(7)darr(b)(4w)/(7)uarr`
Taking torques `w.r.t. 'x'`

`M.I.` of the rod `w.r.t.` axis of rotation
`I_(x)=I_(cm)+(ML^(2))/(16)`
`=(ML^(2))/(12)+(ML^(2))/(15)=(7 ML^(2))/(48)`
`(i) Mg. (L)/(4)=I. alpha`
`Mg.(L)/(4)=(7ML^(2))/(48).alpha`
`rArr alpha=(12g)/(7L), a_(B)=Ra`
`=(3L)/(4).(12g)/(7L)=(9g)/(7) darr`
`(ii) a_(cm)=(L)/(4).alpha=(3g)/(7)`
also apply equation of motion on `COM`
`Mg-N=M.(3g)/(7)`
`N=Mg-(3Mg)/(7)=(4Mg)/(7)uarr`
`[Ans.: (a) (9g)/(7) darr(b)(4w)/(7) uarr ]`
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