Four thin rods, each of mass M and length d=1m are rigidly connected in the form of a positive sign. The entire assembly rotates in a horizontal plane around a vertical axle at the centre with initial (clockwise) angular velocity omega_(i)="2rads"^(-1). A mud ball with mass m and initial speed v_(i)="12 ms"^(-1) is thrown at and sticks to the end of one rod. Let M=3m. What is the final angular velocity omega_(f) of the ''plus sign + mudd ball'' system, if the initial path of the balss is each of the four paths shown in figure

Four thin rods, each of mass M and length d=1m are rigidly connected i

1.	Four thin rods, each of mass M and length d=1m are rigidly connected in the form of a positive sign. The entire assembly rotates in a horizontal plane around a vertical axle at the centre with initial (clockwise) angular velocity omega_(i)="2rads"^(-1). A mud ball with mass m and initial speed v_(i)="12 ms"^(-1) is thrown at and sticks to the end of one rod. Let M=3m. What is the final angular velocity omega_(f) of the ''plus sign + mudd ball'' system, if the initial path of the balss is each of the four paths shown in figure
Answer» Path 1 CONTACT is made when the velocity of the ball is perpendicular to the rod `omega_(f)=-4"rads"^(-1)` Path 2 Radian contact `omega_(f)=-1.6"rads"^(-1)` path 3 perpendicular contact `omega_(f)=0.8"rads"^(-1)` Path 4 contact is made `60^(@)` to the perendicular. Note that all 4 paths are horizontal `omega_(f)=-0.4"rads"^(-1)` Answer :A::B::C::D