A body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2 \,m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is
A body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2 \,m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is
$\frac{1}{2}$ of its initial kinetic energy
$\frac{1}{9}$ of its initial kinetic energy
$\frac{8}{9}$ of its initial kinetic energy
$\frac{1}{4}$of its initial kinetic energy
A body of mass $m$ moving with velocity $v$ makes a head-on collision with another body of mass $2 \,m$ which is initially at rest. The loss of kinetic energy of the colliding body (mass $m$) is
$\frac{{\Delta K}}{K} = \left[ {1 - {{\left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)}^2}} \right] = \left[ {1 - {{\left( {\frac{{m - 2m}}{{m + 2m}}} \right)}^2}} \right]$$ = \frac{8}{9}$
$\Delta K$=$\frac{8}{9}K$i.e. loss of kinetic energy of the colliding body is $\frac{8}{9}$ of its initial kinetic energy.
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