Three particles ( A , B , C ) each of mass m are connected by three massless rods of length l . All three…

Three particles $(\mathrm{A},\mathrm{ }\mathrm{B},\mathrm{ }\mathrm{C})$ each of mass m are connected by three massless rods of length $l$. All three particles lie on a smooth horizontal plane. A particle of mass $m$ moving along one of the rods with velocity $V_0$ strikes on a particle and stops (as shown in the diagram). Tension in any of the rod just after the collision is 

1. $\frac{m{V}_0^2}{36 l}$
2. $\frac{m{V}_0^2}{28 l}$
3. $\frac{m{V}_0^2}{24 l}$
4. $\frac{m{V}_0^2}{12 l}$

Solution

Applying conservation of angular momentum with respect to centroid.

Initial angular momentum = final angular momentum



$r=\frac{l}{2}\mathrm{t}\mathrm{a}\mathrm{n}{30}^o=\frac{l}{2\sqrt{3}}$; $m{V}_0\frac{l}{2\sqrt{3}}=I_{cm}\omega$

$m{V}_0\frac{l}{2\sqrt{3}}=3m{\left(\frac{l}{\sqrt{3}}\right)}^2\omega ; \omega =\frac{V_0}{2\sqrt{3}l}$



$2T\mathrm{c}\mathrm{o}\mathrm{s}{30}^o=m{\omega }^2\frac{l}{\sqrt{3}};T=\frac{m{V}_0^2}{36l}$

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