Momentum and CollisionHard
Question
A particle of mass m moving in XY horizontal plane strikes the end of the vertical rod at an angle 37o with Y-axis. Rod has mass m and length l and it is free to rotate about hinge along Y-axis. If particle strikes rod with speed u and sticks to it, find the CORRECT choice(s).
Options
A.Velocity of particle just after impact will be 
B.Velocity of particle just after impact will be 
C.Minimum speed so that rod completes full rotation about hinge is 
D.Angular momentum of system during collision is conserved about Y-axis.
Solution
Momentum along Y-axis will remain conserved
So, mu cosθ = 2m Vy
⇒ Vy =
....(i)
Conserving angular momentum about Y-axis during collision mu sin θl =
ω
⇒ ω =
....(ii)
Velocity of particle just after impact is
VP = VPĵ + lω(-î) =
ĵ
for completing full rotation about Y-axis
Wg = ᐃk
⇒ - mg(2l) - mgl = 0 -
ω2 ⇒ ωmin = 
= umin = 
So, mu cosθ = 2m Vy
⇒ Vy =
....(i)Conserving angular momentum about Y-axis during collision mu sin θl =
ω ⇒ ω =
....(ii)Velocity of particle just after impact is
VP = VPĵ + lω(-î) =
ĵfor completing full rotation about Y-axis
Wg = ᐃk
⇒ - mg(2l) - mgl = 0 -
ω2 ⇒ ωmin = = umin = Create a free account to view solution
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