question_answer

A spherical ball A of mass 4kg, moving in a straight line strikes another spherical ball B of mass 1kg at rest. After the collision, A and B move with velocities \[{{\operatorname{V}}_{1}}m/s and {{V}_{2}}m/s,\]respectively makes angles of \[30{}^\circ  and 60{}^\circ \] with respect to the original direction of motion of A. the ratio \[\frac{{{\operatorname{V}}_{1}}}{{{V}_{2}}}\] will be:

A) \[\frac{\sqrt{3}}{4}\]                 

B) \[\frac{4}{\sqrt{3}}\]    

C) \[\frac{1}{\sqrt{3}}\]                             

D) \[\sqrt{3}\]

Correct Answer: A

Solution :

When nothing specified, assume collision to be elastic In elastic collision Momentum conserved, K.E. conserved. Momentum conserved in x, y direction \[{{\operatorname{P}}_{{{x}_{1}}}}{{P}_{{{x}_{2}}}}\,and\,\,{{p}_{{{y}_{1}}}}={{p}_{{{y}_{2}}}}\] \[{{p}_{{{y}_{1}}}}={{p}_{{{y}_{2}}}}\] \[4\times 0+1\times 0=4{{v}_{1}}Sin3{{0}^{o}}-{{\operatorname{v}}_{2}}Sin6{{0}^{o}}\] \[{{\operatorname{v}}_{2}}\times \frac{\sqrt{3}}{2}=4{{\operatorname{v}}_{1}}\times \frac{1}{2}\] \[\frac{{{\operatorname{v}}_{1}}}{{{\operatorname{v}}_{2}}}=\frac{\sqrt{3}}{2}\]