Question

A body of mass $2\mathrm{kg}$ makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth its original speed. The mass of the second body which collides with the first body is

• A. $2\mathrm{kg}$
• B. $1.2\mathrm{kg}$
• C. $3\mathrm{kg}$
• D. $1.5\mathrm{kg}$

Hint:

For elastic collisions, $v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For elastic collision, $v_1 = \frac{m_1 - m_2}{m_1 + m_2} u_1$.
Step 2: Detailed Explanation:
Given $v_1 = \frac{u_1}{4}$, so $\frac{m_1 - m_2}{m_1 + m_2} = \frac{1}{4}$. With $m_1 = 2$ kg, $\frac{2 - m_2}{2 + m_2} = \frac{1}{4} \Rightarrow 8 - 4m_2 = 2 + m_2 \Rightarrow 6 = 5m_2 \Rightarrow m_2 = 1.2$ kg.
Step 3: Final Answer:
The mass of the second body is $1.2$ kg.