Question

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 $v_{1}ms^{- 1}andv_{2}ms^{- 1}$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. $\sqrt{3}$

Answer 1

Answer: (A)

$\frac{\sqrt{3}}{4}$

Answer 2

Applying the law of conservation of linear momentum along a direction perpendicular to the direction of motion (i.e. along y - axis), we get

$0 + 0 = 4v_{1}\sin 30^{0} - v_{2}\sin 60^{0}$

$4v_{1}\sin 30^{0} = v_{2}\sin 60^{0}$

$\frac{v_{1}}{v_{2}} = \frac{\sin 60^{0}}{4\sin 30^{0}} = \frac{\sqrt{3}}{4}$