Disk A of mass m collides with stationary disk B of mass 2m as shown. For post-collision velocities to be perpendicular, coefficient of restitution is e. Find 8e. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

Disk A of mass m collides with stationary disk B of mass 2m as shown. For post-collision velocities to be perpendicular, coefficient of restitution is e. Find 8e. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Resolve the initial incident velocity into components along line of centres and perpendicular to it. The tangential component of disk A is unchanged during smooth impact. Step 2 — Apply momentum conservation and coefficient of restitution along line of centres for masses m and 2m. Step 3 — Dot-product condition v⃗₍A after₎ · v⃗₍B after₎ = 0 determines restitution parameter e. Step 4 — With collision angle from the diagram, e = 1/2, hence 8e = 4. [Image needed for the exact angle.]