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A molecule capable of vibrations is modeled as two point atoms of mass $M$ each connected by a spring. Initially molecule is not vibrating. When it collides elastically with a single atom of mass $M$ as shown in figure. Mark the Correct option(s) :

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Velocity of centre of mass of system consisting of atom and molecules is $\frac{2 v_{0}}{3}$

Maximum energy stored in spring after collision is $\frac{M v_{0}^{2}}{4}$

Velocity of centre of mass of molecule after collision is $\frac{v_{0}}{2}$ .

Velocity of atom after collision is $2 v_{0}$ .

answer is A, B, C.

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Detailed Solution

Just after the collision the colliding atom will stop and the collided atomstarts moving with velocity $v_{0 .}$

$v_{c} = \frac{2 M v_{0}}{3 M} = \frac{2 v_{0}}{3}$

$\frac{1}{2} k {x_{m a x}}^{2} = 2 \times \frac{1}{2} M {(v_{0})}^{2} - \frac{1}{2} M {(v_{0})}^{2} - \frac{1}{2} \times 2 M \times {(\frac{v_{0}}{2})}^{2} = \frac{m {v_{0}}^{2}}{4} v'_{c} = \frac{m v_{0}}{2 m} = \frac{v_{0}}{2}$

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