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A nail is fixed at a point P vertically ...

A nail is fixed at a point `P` vertically below the point of suspension 'O' of simple pendulum of length `1 m`. The bob is released when the string of pendulum makes an angle `30^@` with horiozontal. The bob reaches lowest point and then describes vertical circle whose centre coincides with `P` . The least distance of `P` from `O` is

A

`0.4 m`

B

`0.5 m`

C

`0.6 m`

D

`0.8 m`

Text Solution

Verified by Experts

The correct Answer is:
D

If `v` is velocity at the lowest point
`v^(2) = 2gL (1-sin theta)` but, `v^(2) = 5gr & r = L -x`
where `x` is minimum distance between `0` and `P`.
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Knowledge Check

  • A simple pendulum of length l and mass (bob) m is suspended vertically. The string makes an angle theta with the vertical. The restoring force acting on the pendulum is

    A
    `mg tan theta`
    B
    `-mg sin theta`
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  • A simple pendulum of length I and mass (bob) m is suspended vertically. The string makes an angle theta with the vertical. The restoring force acting on the pendulum is

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    `mg tan theta`
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    `-mg sin theta`
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  • A bob hangs from a rigid support by an inextensible string of length l. It is released from rest when string makes an agngle 60^(@) with vertical . The speed of the bob at the lowest position is

    A
    `sqrt( gl)`
    B
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    C
    `sqrt( 2gl)`
    D
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