Question

A body of mass $2kg$ 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 kg
• B. 1.2 kg
• C. 3 kg
• D. 1.5 kg

Answer 1

Answer: (B)

Conservation of linear momentum gives
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\Rightarrow m_2{v}_2=\frac{3u}{2}$
Conservation of kinetic energy gives
$\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2$
$=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2$
$\Rightarrow m_2{v}_2^2=\frac{15u^2}{8}$
Hence, on solving Eqs. (i) and (ii), we get
$m_2=1.2kg$