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Standard XII

Physics

Oblique Collision

A spherical b...

Question

A spherical ball A of mass $4 k g$ , moving in a straight line strikes (elastically) another spherical ball B of mass $1 k g$ at rest. After the collision, balls A and B move with velocities $V_{1}$ m/s and $V_{2}$ m/s respectively, making angles of $30^{\circ}$ and $60^{\circ}$ with respect to the original direction of motion of A. The ratio $\frac{V_{1}}{V_{2}}$ will be:

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

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

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

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$\sqrt{3}$

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Solution

The correct option is A
$\frac{\sqrt{3}}{4}$

In elastic collision
Momentum is conserved and Kinetic Energy is conserved.

Momentum conserved in $x$ and $y$ direction:
$P_{x_{i}} = P_{x_{f}}$
and $P_{y_{i}} = P_{y_{f}} P_{y_{i}} = P_{y_{f}} 4 \times 0 + 1 \times 0 = 4 v_{1} sin 30^{\circ} - v_{2} sin 60^{\circ} v_{2} \times \frac{\sqrt{3}}{2} = 4 v_{1} \times \frac{1}{2} \frac{v_{1}}{v_{2}} = \frac{\sqrt{3}}{4}$

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Similar questions

Q. A spherical ball

A

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4 k g

, moving along a straight line strikes another spherical ball

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The correct option is A √34 In elastic collision Momentum is conserved and Kinetic Energy is conserved. Momentum conserved in x and y direction: Pxi=Pxf and Pyi=PyfPyi=Pyf4×0+1×0=4v1sin30∘−v2sin60∘v2×√32=4v1×12v1v2=√34