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A nail is located below the point of sus...

A nail is located below the point of suspensions of a simple pendlum of length .l.. The bob is released from horizontal position. If the bob loops a verticle circle with nail as centre, find the distance of nail from point of suspension.

Text Solution

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Form the principle of conservation of mechanical energy
PE at the horizontal position = KE at the lowest position.
`mgl = (1)/(2) mv^(2)`
To loop the vertical circle ,
`v^(2)=5g(1-x)` where .x. is the distance of nail from point of suspension, and .v. is the velocity at lowest point of path.
`(mgl=(1)/(2)m.5g (l-x)), l=(5)/(2)(l-x), " " x = 3l//5`
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