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A, B, C are points in a vertical line su...

A, B, C are points in a vertical line such that AB = BC. If a body falls freely from rest at A and `t_(1)` and `t_(2)` are times taken to travel distances AB and BC, then ratio `(t_(2)//t_(1))` is

A

(a) `sqrt(2) + 1`

B

(b) `sqrt(2) -1`

C

(c ) `2sqrt(2)`

D

(d) `1/(sqrt(2) + 1)`

Text Solution

Verified by Experts

The correct Answer is:
(d)
`t_(1) = sqrt(2h/(g))`
`t_(2) =sqrt(4h/(g)) - sqrt(2h/(g))`
`t_(2)/(t_(1)) = sqrt(2h/(g))[sqrt(2) - 1]/(sqrt(2h/(g)) = sqrt(2) - 1`
`:. t_(2)/t_(1) =sqrt(2) - 1 xx sqrt(2) + 1/(sqrt(2)+1) = 1/(sqrt(2) + 1)`
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