Question

A small metal bearing of mass $m_1=30\text{g}$, moving with a velocity of $v_1=25\text{m/s}$ collides elastically with a huge sphere of mass $200\text{kg}$ moving with a velocity of $3\text{m/s}$. What is the velocity of the small metal bearing after colliision?

• A. $9\text{m∕s in original direction}$
• B. $19\text{m∕s opposite to the original direction}$
• C. $9\text{m∕s opposite to the original direction}$
• D. $19\text{m∕s in original direction}$

Answer 1

The correct option is B $19\text{m∕s opposite to the original direction}$

Given:
Mass of small metal bearing;$m_1=30\text{g}=30\times {10}^{-3}\text{kg}$
Mass of huge sphere; $m_2=200\text{kg}$
Initial velocity of small metal bearing ;$u_1=25\text{m/s}$
Initial velocity of huge sphere;$u_2=3\text{m/s}$
Let final velocity of small metal bearing be $v_1$.

From the concept of collision we know
$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\frac{2m_2{u}_2}{m_1+m_2}$
$[\text{As}\frac{m_1}{m_2}<<<1]$
$\Rightarrow v_1=-u_1+2u_2$
$=(-25+2\times 3)\text{m/s}$
$=-19\text{m/s}$
Here $-$ve indicates that small bearing starts moving opposite to its original direction.