Question

In one dimensional elastic collision between a given incoming body A of mass $m_1$ and another body B of mass $m_2$ initially at rest.

• A. B will recoil with greatest speed if $m_2\ll m_1$
• B. B will recoil with greatest Momentum if $m_2\gg m_1$
• C. B will recoil with greatest kinetic energy if $m_1=m_2$
• D. B will recoil with greatest kinetic energy if $m_2=2m_1$

Answer 1

Answer: (A)

B will recoil with greatest speed if $m_2\ll m_1$

Given, $m_1$ and $m_2$ be the masses of $A$ and $B$,
Let,$v_1$ and $v_2$ be the velocities of $A$ and $B$,
$p_1$ and $p_2$ be the momenta of A and B and $p=p_1=p_2$,
$E_1$ and $E_2$ be the kinetic energies of A and B,
Now, if in one dimensional elastic collision between a given incoming body A of mass $m_1$ and another body B of mass $m_2$ initially at rest, then
A will recoil with greatest speed if $m_2\ll m_1$ since,
$p=m_1{v}_1=m_2{v}_2$

$\Rightarrow \frac{m_1}{m_2}=\frac{v_2}{v_1}$ ......(1)

$\Rightarrow m\propto \frac{1}{v}$

$B)B$ will recoil with greatest Momentum if $P_1=P_2$ after collision $A$ will be at rest

$C)B$ will not recoil with greatest kinetic energy if $m_1=m_2$, since, $\frac{m_2}{m_2}=\frac{v_2}{v_1}$............from(1)

$\Rightarrow v_1=v_2$
$\Rightarrow E_1=E_2$

$D)B$ will not recoil with greatest kinetic energy if $m_2=2m_1$, since,

$\frac{m_1}{2m_1}=\frac{v_2}{v_1}$ ..........from(1)

$\Rightarrow 2v_2=v_1$
$\Rightarrow v_1>v_2$
$\Rightarrow E_1>E_2$