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Laws of Motion — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsLaws of Motion3 Marks
Question
one marble collides head$-$on with another identical marble at rest. If the collision is partially inelastic, determine the ratio of their final velocities in terms of coefficient of restitution e.
✓

Answer

According to conservation of momentum,
$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$
As $m_1 = m_2,$ we get, $u_1 + u_2 = v_1 + v_2$
$\therefore$ If $u_2 = 0,$ we get, $v_1 + v_2 = u_1 ….. (i)$
Coefficient of restitution,
$e=\frac{v_2-v_1}{u_1-u_2}$
$\therefore v _2- v _1= eu _1 ......(ii)$
Dividing equation $(i)$ by equation $(ii),$
$\frac{v_1+v_2}{v_2-v_1}=\frac{1}{e}$
Using componendo and dividendo, we get,
$\frac{v_2}{v_1}=\frac{1+e}{1-e}$

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