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.

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KollegeApply · Accepted Answer

B implies A but A does not imply B. If the linear momentum of a system is zero, \Rightarrow m_1 \vec{v}_1 + m_2 \vec{v}_2 + . . . =0 Thus, for a system of comprising two particles of same masses, \vec{v}_1 = - \vec{v}_2 ...(1) The kinetic energy of the system is given by, K . E . = $\frac{1}{2}$m \vec{v}_1^2 + $\frac{1}{2}$m \vec{v}_2^2 Using equation (1) to solve above equation, we can say: K . E . \neq 0 i.e A does not imply B . Now, If the kinetic energy of the system is zero, \Rightarrow $\frac{1}{2}$m \vec{v}_1^2 + $\frac{1}{2}$m \vec{v}_2^2 = 0 v_1 = $\pm$ v_2 On calculating the linear momentum of the system, we get: \vec{P} = m \vec{v}_1 + m \vec{v}_2 \text{ taking v_1 = - v_2 , we can write:} \vec{P} = 0 Hence, we can say, B implies A but A does not imply B.

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