A mass of 1 ; kg collides elastically with a | vedclass

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(A) From the law of conservation of linear momentum:$1 \cdot u = -1 \cdot 2 + 5 \cdot v \implies 5v - 2 = u \quad \dots (i)$From the definition of the

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The total momentum of the system is $3 \; kg \; ms^{-1}$.

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(A) From the law of conservation of linear momentum:$1 \cdot u = -1 \cdot 2 + 5 \cdot v \implies 5v - 2 = u \quad \dots (i)$From the definition of the coefficient of restitution $e$ for an elastic collision $(e=1)$:$1 = \frac{v - (-2)}{u} \implies v + 2 = u \quad \dots (ii)$Solving equations $(i)$ and $(ii)$:$5v - 2 = v + 2 \implies 4v = 4 \implies v = 1 \; ms^{-1}$$u = 1 + 2 = 3 \; ms^{-1}$Evaluating the options:$(A)$ Total momentum of the system $= 1 \cdot u = 1 \cdot 3 = 3 \; kg \; ms^{-1}$. This is correct.$(B)$ Momentum of $5 \; kg$ mass after collision $= 5 \cdot v = 5 \cdot 1 = 5 \; kg \; ms^{-1}$.$(C)$ Kinetic energy of the center of mass is not $0.05 \; J$.$(D)$ Total kinetic energy of the system $= \frac{1}{2} \cdot 1 \cdot u^2 = \frac{1}{2} \cdot 1 \cdot 3^2 = 4.5 \; J$.

$A$ mass of $1 \; kg$ collides elastically with a stationary mass of $5 \; kg$. After the collision,the $1 \; kg$ mass moves in the opposite direction with a velocity of $2 \; ms^{-1}$. Which of the following statements is correct for this system of two masses?

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