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Velocity of CM of two particles is v & the sum of the masses of two particles is m. Kinetic energy of the system :
A. will be = 1/2 mv2
B. will be always less then 1/2 mv2
C. will be greater than or equal to 1/2 mv2
D. will always be greater then 1/2 mv2
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5 Answers
1ans will be (c) ≥ 1/2mv2 as KE as measured in CM's frame is always least.
1ke of the system is NOT the ke of com ..
rather ...it is the sum of ke of all individual particles.
an objective approach :
consider a system : 2 particles each of mass m, one at rest and other with vel v.( same dxn)
ke of the system = 1/2 mv^2
ke of com = 1/2(2m) (v/2)^2 = 1/4 mv^2
this implies ---> ke of system is greater than ke of com ..
consider the same system : but now they both move with vel v ( same dxn)
this time ..u will find that ke of com = ke of system.
hence : ke of system is greater than or equal to ke of com (learn it)
option (c)
1just to add to that, when μ=0 , the compression in the spring is maximum when the kinetic energy of the system is minimum.
i.e velocity of each particle is equal to that of Vcm
