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Consider the following two statements : (A) Linear momentum of a system of particles is zero. B) Kinetic energy of a system of particles is zero. (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: If (B) is true, then ½Σimivi² = 0. In this equation v is magnitude of velocity and m is mass. Mass cannot be zero and square of a scaler quantity can only be zero if it is zero. It means magnitude of velocity of each particle is zero. In that case Σimivi =0. So clearly (B) implies (A). Now if (A) is true, it does not mean that magnitude of each particle is zero. Since linear momentum is a vector, and sum (resultant) of vectors can be zero even if each vector is non-zero. It means momentum of each particle is not zero, hence some of the particles may have non-zero magnitude. In that case (B) is not true. So (A) does not imply (B). |
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