Question

Two object collides elastically mass $2m$ is moving with velocity $U$ and mass $m$ is initially at rest. After the collision, the objects move away with velocities $u$ and $v$, as shown in above figure.
Find the relation between $u$ and $v$?

• A. $2u\cos {30}^o=v\cos {60}^o$
• B. $u\cos {30}^o=2v\cos {60}^o$
• C. $2u\sin {30}^o=v\sin {60}^o$
• D. $u\sin {30}^o=2v\sin {60}^o$
• E. $u\sin {30}^o=v\cos {60}^o$

Answer 1

Answer: (C)

$2u\sin {30}^o=v\sin {60}^o$

Momentum of the system in y direction before collision is zero i.e $P_i=0$

Momentum of the system in y direction after collision $P_f=\left(2m\right)usin{30}^o-mvsin{60}^o$

As the momentum is conserved before and after the collision, thus $P_i=P_f$

$\therefore$ $0=2musin{30}^o-mvsin{60}^o$ $⟹2u$ $sin$ ${30}^o=v$ $sin$ ${60}^o$