Question

A small sized ball A of mass m moves on a smooth horizontal table P with a speed v₁ . O is a fixed sphere of mass M and radius R capable of rotating about a diameter as axis. The ball A jumps from P, comes in contact with sphere and rolls over it without slipping and then jumps to table Q. The linear speed of ball on table Q is v₂ . Then v₂/v₁ is

(1) m/M+m

(2) m/m+2M

(3) 2m/M+3m

(4) 5m/5m+2m

Answer 1

(4) 5m/5m+2m

Regarding ball and sphere as a system; there is no external force and therefore no external torque. The angular momentum of system is conserved. Let v₂ be linear speed of ball as it jumps off to table Q from sphere. Let ω be angular speed accquired by sphere. Since there is no slipping between A and sphere, v₂ = Rω . Using law of conservation of angular momentum (Take angular momentum about point O).