A, B, C and D are points in a vertical line such that AB = BC = CD. If a body falls from rest at A, prove that the time of descent through AB, BC and CD are in the ratio of 1 :— : —.
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
A
Let t 1 , t 2 and t 3 be the times to cover AB, BC and CD
For AB, h = 1/2 gt 1 2
For AC, 2h = 
g (t 1 + t 2 ) 2
For AD, 3h = 
g (t 1 + t 2 + t 3 ) 2
∴ ∴ t 1 : (t 1 + t 2 ) : (t 1 + t 2 + t 3 )
= 1 : √ √ 2 : √ √ 3
Thus t 1 : t 2 : t 3 : : 1 : ( √ √ 2 - 1) : √ √ 3 - √ √ 2.
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