Question

Two identical balls collide head on. The initial velocity of one is $0.75$cm${}^{-1}$. While that of the other is $-0.43$ms${}^{-1}$ . If the collision is perfectly elastic. Their respective final velocities are

• A. $0.75$ ms${}^{-1},-0.43$ ms${}^{-1}$
• B. $-0.43$ ms${}^{-1},0.75$ ms${}^{-1}$
• C. $-0.75$ ms${}^{-1},0.43$ ms${}^{-1}$
• D. $0.43$ ms${}^{-1},0.75$ ms${}^{-1}$

Answer 1

The correct option is B $-0.43$ ms${}^{-1},0.75$ ms${}^{-1}$

In an elastic collision, using momentum conservation and equation for coefficient of restitution, we get,
$v_1=\frac{m_1-m_2}{m_1+m_2}{u}_1+\frac{2m_2}{m_1+m_2}{u}_2$
$v_2=\frac{2m_1}{m_1+m_2}{u}_1+\frac{m_1-m_2}{m_1+m_2}{u}_2$

But $m_1=m_2=m$

$\Rightarrow v_1=\frac{m-m}{m+m}{u}_1+\frac{2m}{m+m}{u}_2,u_2=-0.43$ms${}^{-1}$

$\Rightarrow v_2=\frac{2m}{m+m}{u}_1+\frac{m-m}{m+m}{u}_2,u_1=0.75$ms${}^{-1}$

When two bodies of equal masses undergo elastic collision their velocities get interchanged.