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) :

Engineering

Physics

Question

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

Velocity of atom after collision is 2v₀.

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 $\frac{{Mv}_{0}^{2}}{4}$ .

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

$\frac{1}{2} {kx}_{\max} {}^{2}= \frac{1}{2} {μv}_{rel}^{2} = \frac{1}{2} \times \frac{2 m}{2} \times v_{0} {}^{2}= \frac{{mv}_{0}^{2}}{4}$

$v_{c}^{'} = \frac{{mv}_{0}}{2 m} = \frac{v_{0}}{2}$ .