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A particle of mass m is attached to the ...

A particle of mass m is attached to the celling of a cabin with an inextensible light string of length `l`. The cabin is moving upward with an acceleration a . The particle is taken to a position such that string makes an angle `theta` with vertical. When string becomes vertical, find the tension in the string.

Text Solution

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In a frame associated with cabin.
Work done on the particle when it comes in the vertical position
`=mgl(1-cos theta)+ma l (1-cos theta)`
By work energy theorem,
`(mv^(2))/(2)=(mg l+mal)(1-cos theta)`
`(v^(2))/(2)=(g+a)l(1-cos theta)`
At vertical position,
`T-(mg+ma)=(mv^(2))/(l)`
`T=(mg+ma)+2m(g+a)(1-cos theta)`
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