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For a two - body sstem in absence of ext...

For a two `-` body sstem in absence of external forces, the kinetic energy as measured from ground frame is `K_(0)` and from centre of mass frame is `K_(cm)`. Pick up the wrong statement.

A

The kinetic energy as measured from center of mass frame is least

B

Only the portion of energy `K_(cm)` can be transferred from one form to another due to internal changes in the system.

C

The system always retains at least `K_(o)-K_(cm)` amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system.

D

The system always retains at least `K_(cm)` amount of kinetic energy as measured from ground frame irrespective of any kind of internal changes in the system.

Text Solution

Verified by Experts

The correct Answer is:
D
It can be shown that
`K_(0)=K_(cm)+(1)/(2)WV_(cm)^(2)` where `M` is the total mass of the system and `V_(cm)` is velocity of centre of mass with respect to ground.
Due to internal changes `K_(cm)` can change but `V_(cm)` will remain same. Hence only `K_(cm)` portion of kintic energy can be transformed to some other form of energy. Thus `D` is the wrong statement.
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