Two particles of masses m1 and m2 are connected by a light and inextensible string which passes over a fixed pulley- Initially the particle m1 moves with a velocity -0 when the string is not taut- Neglecting surface- find the velocities of the particles m1 and m2 just after the string is taut-

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Standard XII

Mathematics

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Question

Two particles of masses $m_{1}$ and $m_{2}$ are connected by a light and inextensible string which passes over a fixed pulley. Initially the particle $m_{1}$ moves with a velocity $ν_{0}$ when the string is not taut. Neglecting surface, find the velocities of the particles $m_{1}$ and $m_{2}$ just after the string is taut.

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Solution

During the impact, a large tension develops. The impulse of tension $T_{1}$ is equal to the change in momentum of $m_{1}$ which is given as
$m_{1} ν_{0} - J = m_{1} ν$ (i)
Similarly, the impulse of tension $T_{2}$ is equal to the change in momentum of $m_{2}$ which is given as
$J = m_{2} ν$ (ii)
From Eqs. (i) and (ii), we have
$m_{1} (ν_{0} - ν) = m_{2} ν$
This gives $ν = \frac{m_{1} ν_{0}}{m_{1} + m_{2}}$

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Two particles of masses m1 and m2 are connected by a light and inextensible string which passes over a fixed pulley. Initially the particle m1 moves with a velocity ν0 when the string is not taut. Neglecting surface, find the velocities of the particles m1 and m2 just after the string is taut.