Question

A $32kg$ disc moving with the velocity $v=25m/s$ toward the two stationary discs of mass $8kg$ on a frictionless surface. The discs collide elastically. After the collision, the heavy disc is at rest and the two smaller discs scatter outward with the same speed. What is the $x$-component of the velocity of each of the $8kg$ discs in the final state?

• A. $12.5m/s$
• B. $16m/s$
• C. $25m/s$
• D. $50m/s$
• E. $100m/s$

Answer 1

Answer: (D)

$50m/s$

Given : $m=8$ kg $M=32$ kg $v=25m/s$

Let the x-component of the velocity of each disc be $V$.

Using conservation of momentum in x direction : $P_i=P_f$

$\therefore$ $Mv+0+0=0+mV+mV$ $⟹Mv=2mV$

$\therefore$ $32\times 25=2\times 8V$ $⟹V=50$ $m/s$