Question

A bullet of mass $50\text{gm}$ is fired from a gun towards a ball of mass $450\text{gm}$


The bullet hits the ball with speed $200\text{m/s}$ in horizontal direction as shown in figure, and remains inside it. Find the magnitude of velocity of system of (ball+ bullet) after collision.

• A. $20\text{m/s}$
• B. $10\text{m/s}$
• C. $100\text{m/s}$
• D. $50\text{m/s}$

Answer 1

The correct option is A $20\text{m/s}$

Given, $u_1=200\text{m/s},u_2=0$; where $u_2=$ initial speed of ball
Mass of bullet
$m_1=50\text{gm}$
Mass of ball
$m_2=450\text{gm}$

$\Rightarrow$After collision bullet gets embedded in the ball, hence the system of (ball+bullet) will move together with final speed $v_2\text{m/s}$.

$\therefore$ Applying momentum conservation in horizontal direction, with X-axis taken as:


$P_i=P_f$
$\Rightarrow m_1{u}_1+m_2{u}_2=m_1{v}_2+m_2{v}_2$
$\therefore m_1{u}_1=(m_1+m_2)\times v_2$
Or, $0.05\times 200=(0.05+0.45)v_2$
$\therefore v_2=\frac{10}{0.5}$
$\Rightarrow v_2=20\text{m/s}$