A rod AB of mass M and length L lies on a frictionless horizontal surface. A particle of mass m strikes end A perpendicular to the rod with speed v₀. The collision is perfectly elastic and the particle comes to rest. Which option correctly gives both (i) m/M and (ii) the distance AP of the point on the rod that is instantaneously at rest just after collision?
Options

Question

A rod AB of mass M and length L lies on a frictionless horizontal surface. A particle of mass m strikes end A perpendicular to the rod with speed v₀. The collision is perfectly elastic and the particle comes to rest. Which option correctly gives both (i) m/M and (ii) the distance AP of the point on the rod that is instantaneously at rest just after collision?

Options

G1 Physics · Accepted Answer

Let the particle stop after the elastic collision. Linear momentum gives MV=m v₀. Angular momentum about the rod centre gives Iω=m v₀(L/2), with I=ML²/12. Elastic-energy conservation gives ½mv₀²=½MV²+½Iω². Solving gives m/M=1/4. The instantaneous rest point satisfies V=ωx, giving AP=2L/3. Hence option B.