Question

A body of mass m₁ moving at a constant speed undergoes an elastic head on collision with a body of mass m₂ initially at rest. The ratio of the kinetic energy of mass m₁ after the collision to that before the collision is -

• A. $\left( \frac{m_{1}–m_{2}}{m_{1} + m_{2}} \right)^{2}$
• B. $\left( \frac{m_{1} + m_{2}}{m_{1}–m_{2}} \right)^{2}$
• C. $\left( \frac{2m_{1}}{m_{1} + m_{2}} \right)^{2}$
• D. $\left( \frac{2m_{2}}{m_{1} + m_{2}} \right)^{2}$

Answer 1

Answer: (A)

$\left( \frac{m_{1}–m_{2}}{m_{1} + m_{2}} \right)^{2}$

Answer 2

m₁v₀ = m₂v₂ – m₁v₁ ………(1)

e = $\frac{v_{1} + v_{2}}{v_{0}}$ = 1 ………(2)

Solving (1) and (2)

$\left( \frac{v_{1}}{v_{0}} \right)^{2}$ = $\left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right)^{2}$