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A ball suspended by a thread swing in a...

A ball suspended by a thread swing in a vertical plane that its acceleration values in the lowest possition and the extreme postition are equal . Find the thread deffection angle in the extreme possition.

A

`2 tan^(-1)``(1)/(2)`

B

`tan^(-1)``(1)/(2)`

C

`tan^(-1)sqrt(2)`

D

`tan^(-1)2`

Text Solution

Verified by Experts

The correct Answer is:
A
`a_(A)=g sin theta (` only tangential `)`
`a_(B)=(v^(2))/(l)(` only radial `)`

`K.E.+ P.E. = K.E. + P.E.`
`v^(2)=2gl ( 1- cos theta ) .....(i)`
`:. a_(B)=(v^(2))/(l)=2g(1-cos theta )`
Since, `a_(A)=a_(B)`
`:. g sin theta =2g (1- cos theta )`
`rArr 2 sin`` ( theta )/(2)cos ``(theta)/(2)=2xx2 sin^(2)`` ( theta )/(2)`
`rArr theta =2 tan ^(-1)``((1)/(2))` Ans.
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