Question

A heavy ball moving with speed $v$ collides with a tiny ball. 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. $\frac{v}{3}$

Answer 1

Answer: (B)

$2v$

Using the conservation of momentum and KE, the velocities of the balls after collision is derived.
$m_1=$ mass of the 1st ball
$m_2=$ mass of the 2nd ball
$v_1=$ velocity of the 1st ball before collision$=v$;
$v_2=$ velocity of the 2nd ball before collision$=0$

${v_2}^{{}^{\prime }}=\left(\frac{2m_1}{m_1+m_2}\right)v_1+\left(\frac{m_1-m_2}{m_1+m_2}\right)v_2$;

$m_1>>m_2$;
Substituting $v_1=v$ and $v_2=0$,we get ${v_2}^{\prime }=2v$