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Collision Examples I

Two particles...

Question

Two particles, of masses $M$ and $2 M$ , moving, as shown, with speeds of $10 m/s$ and $5 m/s$ , collide elastically at the origin. After the collision, they move along the indicated directions with speeds $v_{1}$ and $v_{2}$ , respectively. The values of $v_{1}$ and $v_{2}$ are nearly

3.2 m/s

and

12.6 m/s

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3.2 m/s

and

6.3 m/s

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6.5 m/s

and

6.3 m/s

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6.5 m/s

and

3.2 m/s

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Solution

The correct option is C $6.5 m/s$ and $6.3 m/s$
Given:
Speed of mass $M$ particle $= 10 m/s$
Speed of mass $2 M$ particle $= 5 m/s$

Applying conservation of linear momentum in $X$ and $Y$ direction for the system then

$M (10 cos 30 °) + 2 M (5 cos 45 °) = 2 M (v_{1} cos 30 °) + M (v_{2} cos 45 °)$

$5 \sqrt{3} + 5 \sqrt{2} = \sqrt{3} v_{1} + \frac{v_{2}}{\sqrt{2}}$ ... $(1)$
Also

$2 M (5 sin 45 °) - M (10 sin 30 °) = 2 M v_{1} sin 30 ° - M v_{2} sin 45 °$

$5 \sqrt{2} - 5 = v_{1} - \frac{v_{2}}{\sqrt{2}}$ ... $(2)$

Solving equation $(1)$ and $(2)$

$(\sqrt{3} + 1) v_{1} = 5 \sqrt{3} + 10 \sqrt{2} - 5$

$\Rightarrow v_{1} = 6.5 m/s$

$\Rightarrow v_{2} = 6.3 m/s$

Hence option $(A)$ is correct.

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Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds v1 and v2, respectively. The values of v1 and v2 are nearly

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