Three balls are kept on a straight line on a smooth surface. The first ball of mass ${ m }_{ 1 }$ is projected with velocity ${ V }_{ o }$ towards the middle ball of mass ${ m }_{ 2 }$ , which then collides with the third ball of mass ${ m }_{ 3 }$ .

If we want ${ m }_{ 3 }$ to move with the maximum possible velocity, then what should be the mass of ${ m }_{ 2 }$ in kg? All collisions are elastic.

$\textit{Details}$

Use the following data if needed :

$\bullet \quad { m }_{ 1 }\quad =\quad 4\quad kg \\ \bullet \quad { m }_{ 3 }\quad =\quad 9\quad kg \\ \bullet \quad { V }_{ o }\quad =\quad 16\quad m/s$

The answer is 6.

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Use conservation of momentum and newton's experimental law twice to obtain the velocity of ball 3,

$v=\frac { 4{ m }_{ 1 }{ m }_{ 2 } }{ ({ m }_{ 1 }+{ m }_{ 2 })({ m }_{ 2 }+{ m }_{ 3 }) }$

Now use simple calculus , Velocity of ball 3 is maximum when mass of second ball is 6kg.