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Consider the following two statements : (A) Linear momentum of the system remains constant. (B) Centre of mass of the system remains at rest. (a) A implies B and B implies A. (b) A does not imply B and B does not imply A. (c) A implies B but B does not imply A. (d) B implies A but A does not imply B. |
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Answer» (d) B implies A but A does not imply B. Explanation: Position of CoM is given by R =(1/M)Σimiri . If we differentiate both sides w.r.t. time t, we get, dR/dt =(1/M)Σimi.dri/dt vcm=(1/M)Σimivi Now if (B) is true, it means vcm = 0, → Σimivi = 0 =Constant. So (B) implies (A). Now let us check if (A) is true but not equal to zero → Σimivi = k Then vcm=(1/M)k =k/M =not equal to zero. i.e. CoM of the system is not at rest. So (A) does not imply (B). |
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