First slide

Collisions

Question

A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest. After the collision, A and B move with velocities v₁ ms^-1 and v₂ ms^-1 respectively making angles of 30° and 60° with respect to the original direction of motion of A. The ratio $\frac{v_{1}}{v_{2}}$ will be

Moderate

A

$\frac{\sqrt{3}}{4}$
B

$\frac{4}{\sqrt{3}}$
C

$\frac{1}{\sqrt{3}}$
D

$\sqrt{3}$

Solution

Applying the law of conservation of linear momentum along a direction perpendicular to the direction of motion (i.e., along y-axis), we get
$0 + 0 = 4 v_{1} \sin 30^{\circ} - v_{2} \sin 60^{\circ}$
$4 v_{1} \sin 30^{\circ} = v_{2} \sin 60^{\circ} or \frac{v_{1}}{v_{2}} = \frac{\sin 60^{\circ}}{4 \sin 30^{\circ}} = \frac{\sqrt{3}}{4}$

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