Question

A body of mass $2kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

• A. $1.8kg$
• B. $1.0kg$
• C. $1.2kg$
• D. $1.5kg$

Answer 1

The correct option is C $1.2kg$

Step 1: Draw a free body diagram of the given problem

Step 2: Apply the conservation of linear momentum
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
Given, $\text{mass of first body}=2kg$
$\text{Mass of the second body}=m$
Let the mass $2kg$ moves with velocity $v_0$
Conserving linear momentum
$2v_0=2\left(\frac{v_0}{4}\right)+mv$
$2v_0=\frac{v_0}{2}+mv$
$\frac{3v_0}{2}=mv\dots \left(i\right)$

Step 3: Find the mass of the second body
As collosion is elastic so $e=1$
${}^v\text{separation}{=}^v\text{approach}$
$v-\frac{v_0}{4}=v_0$
$\frac{5v_0}{4}=v\dots \left(ii\right)$
Equating $\left(ii\right)$ and $\left(i\right)$
$\frac{3v_0}{2}=m\left(\frac{5v_0}{4}\right)$

$m=\frac{6}{5}=1.2kg$