Question

A particle of mass m₁ moves with speed u₁ and collides head on with a stationary particle of mass m₂. After the collision, the velocities of the particles are v₁ and v₂ and e is coefficient of restitution for the collision. If v₁ is to be positive, i.e., for the first particle to continue moving in the same direction then:

• A. $\frac{m_{2}}{m_{1}} > e$
• B. $\frac{m_{1}}{m_{2}} > e$
• C. $\frac{m_{1} - m_{2}}{m_{2}} > e$
• D. $\frac{m_{1} + m_{2}}{m_{2}} > e$

Answer 1

Answer: (B)

$\frac{m_{1}}{m_{2}} > e$

Answer 2

v₁ > 0

⇒ $\frac{m_{1}u_{1} + m_{2}u_{2} - m_{2}e\left( u_{1} - u_{2} \right)}{m_{1} + m_{2}} > 0$

⇒ m₁ – m₂ e > 0

⇒ $\frac{m_{1}}{m_{2}} > e$