Question
A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass . After collision the $${1^{st}}$$ mass moves with velocity $$\frac{v}{{\sqrt 3 }}$$ in a direction perpendicular to the initial direction of motion. Find the speed of the $${2^{nd}}$$ mass after collision.
A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass . After collision the $${1^{st}}$$ mass moves with velocity $$\frac{v}{{\sqrt 3 }}$$ in a direction perpendicular to the initial direction of motion. Find the speed of the $${2^{nd}}$$ mass after collision.
A.
$$\sqrt 3 v$$
B.
$$v$$
C.
$$\frac{v}{{\sqrt 3 }}$$
D.
$$\frac{2}{{\sqrt 3 }}v$$
Answer :
$$\frac{2}{{\sqrt 3 }}v$$
Solution :
In $$x$$-direction, $$mv = m{v_1}\cos \theta \,......\left( 1 \right)$$
where $${v_1}$$ is the velocity of second mass
In $$y$$-direction, $$\frac{{mv}}{{\sqrt 3 }} = m{v_1}\sin \theta \,......\left( 2 \right)$$
Squaring and adding eqns. (1) and (2)
$$v_1^2 = {v^2} + \frac{{{v^2}}}{{\sqrt 3 }} \Rightarrow {v_1} = \frac{2}{{\sqrt 3 }}v$$
In $$x$$-direction, $$mv = m{v_1}\cos \theta \,......\left( 1 \right)$$
where $${v_1}$$ is the velocity of second mass
In $$y$$-direction, $$\frac{{mv}}{{\sqrt 3 }} = m{v_1}\sin \theta \,......\left( 2 \right)$$
Squaring and adding eqns. (1) and (2)
$$v_1^2 = {v^2} + \frac{{{v^2}}}{{\sqrt 3 }} \Rightarrow {v_1} = \frac{2}{{\sqrt 3 }}v$$
