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Figure shows the system of two masses m and 2m that are connected by a string of length 2l.
This system is placed on a smooth horizontal surface.

Initially masses are separated by a distance l and mass 2m is given a velocity v.

when the string is taut , mass 2m will be in circular motion as shown in figure .

Speed w of mass 2m just after the string is taut is determined by conservation of angular momentum.

initial angular momentum just before string is taut = ( 2m) × v × sin30 = m v

Angular momentum just after string is taut = I ω  =  = ( 4 × m × l × w )
where I is moment of inertia of system about the axis passing through mass m  and
ω is angular speed of mass 2m just after string is taut.

( 4 × m × l × w ) = ( m v )

w = v / (4l)
Answered by Thiyagarajan K | 15 Jan, 2023, 09:10: AM

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