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A sphere is suspended by a thread of len...

A sphere is suspended by a thread of length l. What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension?

A

`sqrt( gl)`

B

`gl`

C

`2 gl`

D

`sqrt(2 gl)`

Text Solution

Verified by Experts

The correct Answer is:
D

Let v be the horizontal velocity given to the sphere at A .
At A, Its K.E` =(1)/(2) mv^(2) and P.E =0`
when it reaches , the height of suspension ,it is at B , where
`therefore ` by the prienciple of conservation of energy
`(1)/(2)mv^(2) = mg h = mg L`
`therefore v^(2) = 2 gh or v= sqrt(2gL)`
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Knowledge Check

  • A sphere is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

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

  • A spere is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension?

    A
    `sqrt("5 gl")`
    B
    2 gl
    C
    `sqrt(gl)`
    D
    `sqrt(2gl)`

  • The bob of a simple prendulum is suspended by a strinng of length 80 cm . What minimum horizontal velocity should be imparted to the bob so that it reaches it reaches the height of suspension point ? (g=10 m//s^(2))

    A
    `3m//s`
    B
    `4m//s`
    C
    `2m//s`
    D
    `5m//s`

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