A mass m moves with a velocity $$nu$$ and collides inelastically with another identical mass .After collision the first 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 $\nu$ and collides inelastically with another identical mass .After collision the first mass moves with velocity in a direction perpendicular to the initial direction of motion.Find the speed of the 2^nd mass after collision

Option 1)
$\frac{2}{\sqrt{3}}\nu$
Option 2)
$\frac{\nu }{\sqrt{3}}$

Option 3)
$\nu$
Option 4)
$\sqrt{3}\nu$

Answers (1)

P perimeter

As we learnt in

Elastic Collision in 2 dimension -

$\fn_jvn \vec{P_{i}}= \vec{P_{f}}$

$m_{1}v_{0}\: \: \hat{i}= \left ( m_{1}v_{1} \cos \Theta + m_{2}v_{2} \cos \beta \right )\hat{i}+\left ( m_{1}v_{1} \sin \Theta - m_{2}v_{2} \sin \beta \right )\hat{j}$

- wherein

From conservation of momentum

Along x - direction P_xi = P_xf

$mv=mv_{1}\cos \theta$ .........(1)

Along y - direction

$0=mv_{1}\ sin\theta+\frac{mv}{\sqrt{}3}$ .........(2)

v₁ & $\theta$ are speed and angle of inclination for 2^nd mass.

$v_{1}\ sin\theta=-\frac{v}{\sqrt{}3}$

$v_{1}\ cos\theta=v$

Square and add the two equation

$v^{2}+\frac{v^2}{3}=v_{1}^{2}\ \Rightarrow\ v_{1}=\frac{2}{\sqrt{}3}v$

Correct answer is 1

Option 1)

$\frac{2}{\sqrt{3}}\nu$

This is the correct option.

Option 2)

$\frac{\nu }{\sqrt{3}}$

This is an incorrect option.

Option 3)

$\nu$

This is an incorrect option.

Option 4)

$\sqrt{3}\nu$

This is an incorrect option.

Option 1) $\frac{2}{\sqrt{3}}\nu$	Option 2) $\frac{\nu }{\sqrt{3}}$
Option 3) $\nu$	Option 4) $\sqrt{3}\nu$

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A mass m moves with a velocity and collides inelastically with another identical mass .After collision the first mass moves with velocity in a direction perpendicular to the initial direction of motion.Find the speed of the 2nd mass after collision Option 1) Option 2) Option 3) Option 4)

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