Question

A massive ball moving with speed $v$ collides with a tiny ball having a mass very much smaller than the mass of the first ball. If the collision is elastic, then immediately after the impact, the second ball will move with a speed approximately equal to:

• A. $v$
  
• B. $2v$
  
• C. $\frac{v}{2}$
  
• D. infinite

Answer 1

The correct option is B $2v$

By momentum conversation.

$MV+0={MV}_1+m{V}_2$

$M(V-V_1)=m{V}_2⟶\left(1\right)$

By energy conservation.

$\frac{1}{2}M{V}^2+0=\frac{1}{2}M{V}_1^2+\frac{1}{2}m{V}_2^2$

$\Rightarrow M{V}^2=M{V}_1^2+m{V}_2^2$

$M(V^2-V_1^2)=m{V}_2^2⟶\left(II\right)$

Dividing (II) by (I)

$\frac{V^2-V_1^2}{V-V_1}=+V_2$

$V+V_1=V_2$ putting in (II)

$V_1=(M_1-m_2)V/M+m_1$

$V_2=2MV/(M+m)\because M>>m$

$\therefore M+m\approx M$

$V_2=2V$