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A partical falls from a height h upon a...

A partical falls from a height `h` upon a fixed horizontal plane and rebounds. If `e` is the coefficient of restitution, the total distance travelled before rebounding has stopped is

A

`h((1+e^2)/(1-e^2))`

B

`h((1-e^2)/(1+e^2))`

C

`h/2((1-e^2)/(1+e^2))`

D

`h/2((1+e^2)/(1-e^2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Total distance travelled by ball before it stops rebounding -
`H=h_0+2h_1+2h_3+ "- - - -"=`
`=h_0+2e^2h_(0)+2e^(4)h_(0)+ "- - - -"`
`H=h_0[1+2e^2][1+^2+e^4+"- - - -"]`
`h_0[1+2e^2] [1/(1-e^2)]`
`H=h_0[(1+e^2)/(1-e^2)]=h[(1+e^2)/(1-e^2)]`
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Knowledge Check

  • A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is :

    A
    `h((1+e^(2))/(1-e^(2)))`
    B
    `h((1-e^(2))/(1+e^(2)))`
    C
    `(h)/(2) ((1-e^(2))/(1+e^(2)))`
    D
    `(h)/(2) ((1+e^(2))/(1-e^(2)))`

  • A particle falls from a height h on a fixed horizontal plate and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is

    A
    `(h(1 + e^2))/((1 - e^2))`
    B
    `(h(1 - e^2))/((1 + e^2))`
    C
    `(h(1 - e^2))/(2(1 + e^2))`
    D
    `(h(1 + e^2))/(2(1 - e^2))`

  • A ball falls from a height h upon a fixed horizontal plane, e is the coefficient of restitution, the whole distance described by the ball before it comes to rest is

    A
    `(1+e^(2))/(1-e^(2))h`
    B
    `(1-e^(2))/(1+e^(2))h`
    C
    `(1+e^(2))/((1-e^(2))h)`
    D
    `(1-e^(2))/((1+e^(2))h)`