An object of mass m_{1} collides with another | vedclass

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(A) Let the initial velocity of mass $m_{1}$ be $u$ and the final velocities of $m_{1}$ and $m_{2}$ be $v$ in opposite directions. Since the collision

Vedclass · Accepted Answer

$3:1$

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(A) Let the initial velocity of mass $m_{1}$ be $u$ and the final velocities of $m_{1}$ and $m_{2}$ be $v$ in opposite directions. Since the collision is elastic (implied by the context of such problems),we use the conservation of linear momentum and the coefficient of restitution.Conservation of linear momentum:$m_{1}u = m_{2}v - m_{1}v$$m_{1}u = v(m_{2} - m_{1})$  --- $(1)$Coefficient of restitution $e = 1$ for elastic collision:$e = \frac{v_{sep}}{v_{app}} = \frac{v - (-v)}{u - 0} = 1$$2v = u$  --- $(2)$Substitute $u = 2v$ into equation $(1)$:$m_{1}(2v) = v(m_{2} - m_{1})$$2m_{1} = m_{2} - m_{1}$$m_{2} = 3m_{1}$$\frac{m_{2}}{m_{1}} = 3$Thus,the ratio $m_{2} : m_{1}$ is $3:1$.

An object of mass $m_{1}$ collides with another object of mass $m_{2}$,which is at rest. After the collision,the objects move with equal speeds in opposite directions. The ratio of the masses $m_{2} : m_{1}$ is

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