question_answer

A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest. After the collision, A and B move with velocities \[{{v}_{1}}\,m{{s}^{-1}}\]and \[{{v}_{2}}\,m{{s}^{-1}}\] respectively making angles of \[{{30}^{o}}\] and \[{{60}^{o}}\] with respect to the original direction of motion of A. The ratio \[\frac{{{v}_{1}}}{{{v}_{2}}}\] will be

A)  \[\frac{\sqrt{3}}{4}\]

B)  \[\frac{4}{\sqrt{3}}\]

C)  \[\frac{1}{\sqrt{3}}\]

D)  \[\sqrt{3}\]

Correct Answer: A

Solution :

Along y-axis momentum remains zero. Here \[4{{v}_{1}}\sin {{30}^{o}}={{v}_{2}}\sin {{60}^{o}}\] \[=1+8+16+64=89\]