Question

A metallic ball of mass $20\text{kg}$ moving with a velocity of $5\text{m/s}$ collides with a small plastic ball of mass $5\text{g}$ initially at rest. What is the final velocity of the plastic ball?

• A. $10\text{m/s}$
• B. $5\text{m/s}$
• C. $0\text{m/s}$
• D. $15\text{m/s}$

Answer 1

The correct option is A $10\text{m/s}$

Given:
Mass of metallic ball; $m_1=20\text{kg}$
Mass of plastic ball;$m_2=5\text{g}=5\times {10}^{-3}\text{kg}$
Initial velocity of metalic ball;$u_1=5\text{m/s}$
Initial velocity of plastic ball;$u_2=0\text{m/s}$

Let final velocity of plastic ball is $v_2$.
From the concept of collision we know,
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$(m_1\times 5)+(m_2\times 0)=m_1{v}_1+m_2{v}_2$
Divide above equation by $m_1$
$5=v_1+\frac{m_2}{m_1}{v}_2$
As, $\frac{m_2}{m_1}=\frac{5}{20000}\approx 0$
$v_1=5\text{m/s}\dots \left(1\right)$

As we know,
$u_1-u_2=v_2-v_1$
$5=v_2-5$
$v_2=10\text{m/s}$