Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassCollisionHard2 minPYQ_2017

PhysicsHardsingle choice

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in figure. They collide completely inelastic and move as a single particle $C$ . The angle $θ$ that the path of $C$ makes with the $X$ -axis is given by-

Options:

Answer:

Solution:

After inelastic collision mass of the combination is $2m$

$v'$ be the velocity of the combined mass

Using conservation of momentum along $X$ and $Y$ -axis

$2 m v^{'} \sin θ = \frac{m v}{\sqrt{2}} + \frac{m v \sqrt{3}}{2}$

$2 m v^{'} \cos θ = \frac{m v}{2} - \frac{m v}{\sqrt{2}}$

$\frac{2 sinθ}{2 cosθ} = \frac{\frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2}}{\frac{1}{2} - \frac{1}{\sqrt{2}}} = \frac{\sqrt{2} + \sqrt{3}}{1 - \sqrt{2}}$

$\tan θ = \frac{\sqrt{2} + \sqrt{3}}{1 - \sqrt{2}}$

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Collision

⏱ 2mℹ️ Source: PYQ_2017

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