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A rectangular billiard table has dimensions AB = $4 \sqrt{3}$ feet and BC = 2 feet. Ball 1 is at the centre of the table. Ball 2 moving perpendicular to CD hits ball 1. After the collision ball 2 itself goes straight into the hole at A. Assume that the balls are identical and their dimensions are too small compared to the dimensions of a hole. All collisions are elastic .

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The ball 1 will fall into the hole at C

The balls will move right angle to each other

The ball 1 will fall into the hole D

The angle between the balls after collision will be 30⁰

answer is A, B.

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Detailed Solution

Path of the two balls after collision has been shown in figure
$\tan α = \frac{2 \sqrt{3}}{2} = \sqrt{3} \Rightarrow α = 60^{\circ}$

Since it is elastic collision between two identical balls both of them will travel at right angle to each other

$∴ β = 30^{\circ}$
$∴ ED = 2 \tan 30^{\circ} = \frac{2}{\sqrt{3}} and DB = 4 \tan 30^{\circ} = \frac{4}{\sqrt{3}} ∴ EB = \frac{6}{\sqrt{3}} = 2 \sqrt{3}$
$\Rightarrow$ The ball 1 will fall into the hole at C.

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