A shell in free space initially at rest explo | vedclass

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Question

(A) Since there are no external forces acting on the shell,the linear momentum of the system is conserved. Initially,the shell is at rest,so the initi

Vedclass · Accepted Answer

Both have the same momentum after the explosion

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(A) Since there are no external forces acting on the shell,the linear momentum of the system is conserved. Initially,the shell is at rest,so the initial momentum is $0$. Therefore,the final momentum of the two pieces must also be $0$. Let $m_A$ and $m_B$ be the masses of pieces $A$ and $B$,and $v_A$ and $v_B$ be their velocities. Then,$m_A v_A + m_B v_B = 0$,which implies $m_A v_A = -m_B v_B$. This means the magnitudes of their momenta are equal: $|p_A| = |p_B|$. Thus,option $A$ is correct. Regarding kinetic energy,$K = p^2 / (2m)$. Since $|p_A| = |p_B| = p$,we have $K_A = p^2 / (2m_A)$ and $K_B = p^2 / (2m_B)$. Given $m_A  K_B$. Therefore,piece $A$ has greater kinetic energy.

$A$ shell in free space initially at rest explodes into two pieces,$A$ and $B$,which then move in opposite directions. Piece $A$ has less mass than piece $B$. Ignore all external forces. Identify the correct statement.

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