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Velocity of Separation and Approach

Two object co...

Question

Two object collides, mass $2 m$ is moving with velocity $U$ and mass $m$ is initially at rest. After the collision, the objects move away with velocities $u$ and $v$ , as shown in above figure
If the collision is elastic, then

U^{2} = u^{2} - \frac{1}{2 v^{2}}

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{2 U}^{2} = \frac{3}{2} u^{2} + \frac{1}{4 v^{2}}

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U = u - \frac{1}{2 v}

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U = u + \frac{1}{2 v}

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{(U - u)}^{2} = \frac{1}{2 v^{2}}

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Solution

The correct option is B ${2 U}^{2} = \frac{3}{2} u^{2} + \frac{1}{4 v^{2}}$
For elastic collision, the kinetic energy is conserved.
Kinetic energy conservation along horizontal:
$\frac{1}{2} (2 m) U^{2} + \frac{1}{2} m 0^{2} = \frac{1}{2} (2 m) (u cos 30^{o})^{2} + \frac{1}{2} m (v cos 60^{o})^{2}$
or $2 m U^{2} = 2 m u^{2} (\frac{\sqrt{3}}{2})^{2} + m v^{2} (1 / 2)^{2}$
or $2 U^{2} = (3 / 2) u^{2} + (1 / 4) v^{2}$

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Two object collides, mass 2m is moving with velocity U and mass m is initially at rest. After the collision, the objects move away with velocities u and v, as shown in above figureIf the collision is elastic, then

The correct option is B 2U2=32u2+14v2For elastic collision, the kinetic energy is conserved. Kinetic energy conservation along horizontal:12(2m)U2+12m02=12(2m)(ucos30o)2+12m(vcos60o)2or 2mU2=2mu2(√32)2+mv2(1/2)2or 2U2=(3/2)u2+(1/4)v2

Two object collides, mass $2 m$ is moving with velocity $U$ and mass $m$ is initially at rest. After the collision, the objects move away with velocities $u$ and $v$ , as shown in above figure
If the collision is elastic, then