A ball moving with velocity 2 , m/s collides | vedclass

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(A) Given: $m_1 = m$,$m_2 = 2m$,$u_1 = 2 \, m/s$,$u_2 = 0$,and $e = 0.5$.Applying the law of conservation of linear momentum:$m_1 u_1 + m_2 u_2 = m_1

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$0, 1$

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(A) Given: $m_1 = m$,$m_2 = 2m$,$u_1 = 2 \, m/s$,$u_2 = 0$,and $e = 0.5$.Applying the law of conservation of linear momentum:$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$m(2) + 2m(0) = m v_1 + 2m v_2$$2m = m v_1 + 2m v_2 \implies v_1 + 2v_2 = 2$ $...(i)$Using the definition of the coefficient of restitution:$e = \frac{v_2 - v_1}{u_1 - u_2}$$0.5 = \frac{v_2 - v_1}{2 - 0}$$v_2 - v_1 = 1$ $...(ii)$Adding equations $(i)$ and $(ii)$:$(v_1 + 2v_2) + (v_2 - v_1) = 2 + 1$$3v_2 = 3 \implies v_2 = 1 \, m/s$Substituting $v_2 = 1$ into equation $(ii)$:$1 - v_1 = 1 \implies v_1 = 0 \, m/s$Thus,the velocities after collision are $0 \, m/s$ and $1 \, m/s$.

$A$ ball moving with velocity $2 \, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$,then their velocities (in $m/s$) after collision will be

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