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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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