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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power3 Marks
Question
What is an elastic collision? What will happen, when
  1. A heavy body collides with a light mass at rest.
  2. A light body collides with a heavy mass at rest.
✓

Answer

Elastic collision is one in which both momentum and energy are conserved. We know, when two bodies $m_1$ and $m_2$ moving with velocities $u_1$ and $u_2$​​​​​​​ collide, their velocities become, $\text{v}_1=\frac{(\text{m}_1-\text{m}_2)\text{u}_1+2\text{m}_2\text{u}_2}{\text{(m}_1+\text{m}_2}$ $\text{v}_2=\frac{\text{m}_2-\text{m}_1)\text{u}_2+2\text{m}_1\text{u}_1}{(\text{m}_1+\text{m}_2)}$
  1. if $m_1 >> m_2$ and $u_2 = 0$, we get
$\text{v}_1=\frac{\text{m}_1\text{u}_1}{\text{m}_1}=\text{u}_1,\text{v}_2=2\text{u}_1$
  1. If $m_1 >> m_2​​​​​​​$​​​​​​​ and $u_1 = 0$, we get
$\text{v}_1=\frac{2\text{m}_2\text{u}_2}{\text{m}_1}, $ as $m_2 << m_1​​​​​​​$
$\therefore\text{v}_1\approx0$
$\text{v}_2=-\frac{\text{m}_1\text{u}_2}{\text{m}_1}=-\text{u}_2$

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