SATHEE: Kinematics Question 403

Kinematics Question 403

Question: Let A, B, C, D be points on a vertical line such that AB = BC = CD. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio.

Options:

A) $1 : \sqrt{3} - \sqrt{2} : \sqrt{3} + \sqrt{2}$

B) $1 : \sqrt{2} - 1 : \sqrt{3} - \sqrt{2}$

C) $1 : \sqrt{2} - 1 : \sqrt{3}$

D) $1 : \sqrt{2} : \sqrt{3} - 1$

Show Answer

Answer:

Correct Answer: B

Solution:

$S=AB= \frac{1}{2} g {t_{1}}^{2}$
$\Rightarrow 2S=AC= \frac{1}{2} g {(t_{1} + t_{2})}^{2}$

$and 3S = AD = \frac{1}{2} G {(t_{1} + t_{2} + t_{3})}^{2}$

$t_{1} = \sqrt{\frac{2 S}{g}}$

$t_{1} + t_{2} = \sqrt{\frac{4 S}{g}}, t_{2} = \sqrt{\frac{4 S}{g}} - \sqrt{\frac{2 S}{g}}$

$t_{1} + t_{2} + t_{3} = \sqrt{\frac{6 S}{g}}, t_{3} = \sqrt{\frac{6 S}{g}} - \sqrt{\frac{4 S}{g}}$

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

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Kinematics Question 403

Question: Let A, B, C, D be points on a vertical line such that AB = BC = CD. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio.

Options:

Answer:

Solution:

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