The sphere A of mass m moving with a constant | vedclass

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(C) Let the initial velocity of sphere $A$ be $u$ and the final velocities of spheres $A$ and $B$ be $v_1$ and $v_2$ respectively.By the law of conser

Vedclass · Accepted Answer

$1:7$

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(C) Let the initial velocity of sphere $A$ be $u$ and the final velocities of spheres $A$ and $B$ be $v_1$ and $v_2$ respectively.By the law of conservation of linear momentum:$m u + (2m)(0) = m v_1 + 2m v_2$$u = v_1 + 2v_2$  ....$(i)$Given the coefficient of restitution $e = 0.4 = \frac{2}{5}$.Using the definition of the coefficient of restitution:$e = \frac{v_2 - v_1}{u_1 - u_2} = \frac{v_2 - v_1}{u - 0} = 0.4$$v_2 - v_1 = 0.4u$  ....$(ii)$From equation $(i)$,$u = v_1 + 2v_2$. Substitute this into equation $(ii)$:$v_2 - v_1 = 0.4(v_1 + 2v_2)$$v_2 - v_1 = 0.4v_1 + 0.8v_2$$0.2v_2 = 1.4v_1$$\frac{v_1}{v_2} = \frac{0.2}{1.4} = \frac{1}{7}$

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is

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