Question

body a of mass 2kg collides with the another body b at rest initially. the collision is perfectly elastic. after collision body a continues to move in its original direction with the speed one-fourth of its original speed. calculate the mass of body b :

Answer 1

The mass of body B, given that the collision is perfectly elastic is 6 Kg

How to calculate the mass of body B?

The mass of body B, given that the collision is perfectly elastic can be calculated as follow:

• Mass of body A (m₁) = 2 Kg
• Initial speed of body A (u₁) = u
• Initial speed of body B (u₂) = 0 m/s
• Speed of bodies after collision (v) = one-fourth original speed =
  `(u)/(4)`
• Mass of body B (m₂) = ?

`(m_1u_1)\ +\ (m_2u_2) = v(m_1\ +\ m_2)\\\\(2\ *\ u)\ +\ 0 = (u)/(4) (2\ +\ m_2)\\\\2u = (u)/(4) (2\ +\ m_2)\\\\2 = (1)/(4) (2\ +\ m_2)\\\\2\ *\ 4 = 2\ +\ m_2\\\\8 = 2\ +\ m_2\\\\Collect\ like\ terms\\\\m_2 = 8\ -\ 2\\\\m_2 = 6\ Kg`

Thus, from the above calculation, we see that the mass of body B is 6 Kg