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A particle is released from a height S. ...

A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

A

`(h)/(3),sqrt((2gh)/(3))`

B

`(h)/(3),2sqrt((gh)/(3))`

C

`(2h)/(3)sqrt((2gh)/(3))`

D

`(h)/(3)sqrt(2gh)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • A particle is released from a height h. At a certain height, its kinetic energy is two times its potential energy. Height and speed of the particle at that instant are

    A
    `h/3 sqrt((2gh)/(3))`
    B
    `h/3 2sqrt((gh)/(3))`
    C
    `(2h)/3 sqrt((2gh)/(3))`
    D
    `h/3 sqrt(2gh)`

  • A particle is dropped from height H. At a point its kinetic energy is x times of its potential energy. Find the speed of the particle at that point -

    A
    `[2gxH]^(1//2)`
    B
    `[(2g(x+1)H)/(x)]^(1//2)`
    C
    `[(2gH)/((x+1))]^(1//2)`
    D
    `[(2gxH)/((x+1))]^(1//2)`

  • A particle is realesed from a height H from ground. At certain height its kinetic energy is three times its gravitational potential energy with respect to ground. Then choose the correct option(s). (Given 'g' is acceleration due to gravity is constant).

    A
    The height of the particle at that instant is `(H)/(2)`
    B
    The height of the particle at that instant is `(H)/(4)`
    C
    The speed of the particle at that instant is `sqrt((3gH)/(2))`
    D
    The speed of the particle at that instant is `(sqrt(3gH))/(2)`

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