Center of MassHard
Question
A train of mass M is moving on a circular track of radius ′R′ with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be
Options
A.0
B.
C.MVR
D.MV
Solution
(B) If we treat the train as a ring of mass ′M′ then its COM will be at a distance from the centre of the circle. Velocity of centre of mass is :
VCM = RCM .ω
=
.ω = 
(∵ ω = 
)
⇒ VCM =
⇒ MVCM = 
As the linear momentum of any system = MVCM
∴ The linear momentum of the train =
VCM = RCM .ω
=
.ω = (∵ ω = )⇒ VCM =
⇒ MVCM = As the linear momentum of any system = MVCM
∴ The linear momentum of the train =
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