two balls of masses m and 2m moving in opposite direction collides hea – InterviewSolution

1.	two balls of masses m and 2m moving in opposite direction collides head on elastically with velocity v and 2v . find their velocities after collision
Answer» Mass of 1st ball , $m_1$ = m mass of 2nd ball, $m_2$ = 2m initial velocity of 1st ball , $u_1$ = -v initial velocity of 2nd ball, $u_2$ = 2v use law of CONSERVATION of linear momentum, $m_1u_1+m_2u_2=m_1v_1+m_2v_2$ $-mv+4mv=m(v_1+2v_2)$ $3v=v_1+2v_2$ ......(1) use law of conservation of ENERGY, $\frac{1}{<klux>2</klux>}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$ $mv^2+(2m)(2v)^2=m(v_1^2+2v_2^2)$ $9v^2=v_1^2+2v_2^2$ .....(2), from equations (1) and (2), $v_1=-v$ and $v_2=2v$

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