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A bob of mass m suspended by a light str...

A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure . What will be the trajectory of the particle if the string is cut at
(a) Point B ? (b) Point C? (c) Point X?

A

` theta = (pi)/( 4)`

B

` (pi)/( 4) lt theta lt (pi)/( 4)`

C

` (pi)/( 2) lt theta lt ( 3 pi)/( 4)`

D

` ( 3 pi)/( 4) lt theta lt pi`

Text Solution

Verified by Experts

The correct Answer is:
D
`v^(2) = u^(2) - 2gh rArr ( 5 gL)/( 4) = 5 gL - 2 gL (1 - cos theta )`
`rArr 5 = 20 - 8 (1 - cos theta )`

`cos theta = (-7)/( 8) : ( 3 pi)/( 4) lt theta lt pi`
`rArr cos theta = - 0.875`
`cos ((3 pi)/( 4)) = - (1)/( sqrt(2)) = - 0.707 and cos (pi) = - 1 `
Hence ` - 0.707 lt theta lt - 1 `
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