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 2nd 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)

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 Pxi = Pxf

    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 2nd 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.

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