Question

a body of mass 1 kg makes an elastic collision with another body at rest continues to move in the word malediction after collision with a velocity equal to 1/5th of the original velocity find the mass of the second body​

Answer 1

Since the collision is elastic, the final velocity of the first body will be,

$v_1=\left (\dfrac{m_1-m_2}{m_1+m_2}\right)u_1+\left (\dfrac {2m_2}{m_1+m_2}\right)u_2$

But, in the question,

$m_1=1\ \text{kg}\\\\u_2=0\ \mathrm {ms^{-1}}\\\\v_1=\dfrac {1}{5}u_1$

We have to find $m_2.$

Then,

$\dfrac {1}{5}u_1=\left (\dfrac{1-m_2}{1+m_2}\right)u_1\\\\\\\dfrac{1-m_2}{1+m_2}=\dfrac {1}{5}\\\\\\5(1-m_2)=1+m_2\\\\\\5-5m_2=1+m_2\\\\\\6m_2=4\\\\\\\mathbf {m_2=\dfrac {2}{3}\ kg}$