Question

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. $\left( \sqrt{2 - 1} \right):\left( \sqrt{3} - \sqrt{2} \right)$
• B. $\left( \sqrt{3} - 1 \right):\left( \sqrt{3} - \sqrt{2} \right)$
• C. $\left( \sqrt{3} - \sqrt{2} \right):\left( \sqrt{2} - 1 \right)$
• D. $\left( 1 - \sqrt{2} \right):\left( \sqrt{2} - \sqrt{3} \right)$

Answer 1

Answer: (A)

$\left( \sqrt{2 - 1} \right):\left( \sqrt{3} - \sqrt{2} \right)$

Answer 2

Let t₁, t₂ and t₃ be the times to cover AB, BC and CD

For AB, h = 1/2 gt₁²

For AC, 2h = $\frac{1}{2}$ g(t₁ + t₂)²

For AD, 3h = $\frac{1}{2}$ g(t₁ + t₂ + t₃)²

∴ t₁: (t₁ + t₂) : (t₁ + t₂ + t₃)

= 1 : √2 : √3

Thus t₁ : t₂ : t₃ : : 1 : (√2 - 1) : √3 - √2.