A small ball moves towards right with a speed v. It collides with the fixed walls and bounces back and forth on the horizontal frictionless surface. If the average speed during the first round trip – i.e. travelling first from A to B and then from B to A – is (2/3)v, find the coefficient of restitution of impact in multiples of 10⁻¹.
Physics · Mixed Chapter
JEE Mains

Question

A small ball moves towards right with a speed v. It collides with the fixed walls and bounces back and forth on the horizontal frictionless surface. If the average speed during the first round trip – i.e. travelling first from A to B and then from B to A – is (2/3)v, find the coefficient of restitution of impact in multiples of 10⁻¹.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let wall spacing be d. Outgoing speed after the bounce at B is ev. The first round-trip distance is 2d, time is d/v + d/(ev). Step 2: Average speed is 2d/[d/v+d/(ev)]=2ev/(1+e). It is given as 2v/3. Step 3: 2e/(1+e)=2/3 ⇒3e=1+e ⇒e=1/2=5×10⁻¹. Step 4: Requested coefficient in multiples of 10⁻¹ is 5.