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A stone tied to a string of length L is ...

A stone tied to a string of length `L` is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at lowest position and has a speed `u` . Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.

A

`=sqrt( 2(u^(3)-gL))`

B

`=sqrt( 2(u^(2)-L))`

C

`=sqrt( 3(u^(2)-gL))`

D

`=sqrt( 2(u^(2)-gL))`

Text Solution

Verified by Experts

The correct Answer is:
D
`v=sqrt(u^(2)-2gh)=sqrt(u^(2)-2gL)`
`|DeltaV|=|v_(f)-v_(i)|`
`=sqrt(v^(2)+u^(2)-2v.ucos90^(@))`
`=sqrt((u^(2)-2gH)+u^(2))`
`=sqrt( 2(u^(2)-gL))`
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Knowledge Check

  • A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

    A
    `sqrt(u^(2) - 2gL)`
    B
    `sqrt2gL`
    C
    `sqrt(u^(2) - gL)`
    D
    `sqrt(2(u^(2) - gL)`

  • A stone tied to a string of length L is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of change in its velocity as it reaches a position, where the string is horizontal is

    A
    `sqrt( u^2 -2 gL)`
    B
    `sqrt(2gL)`
    C
    `sqrt(u^2 - gL)`
    D
    `sqrt(2(u^2 -gL))`

  • A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is

    A
    `sqrt(2(u^(2)-gl)`
    B
    `sqrt(u^(2)=gl)`
    C
    `u-sqrt(u^(2)=2gl)`
    D
    `sqrt(2gl)`

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