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CBSE Class 11-science Answered

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Asked by gdeadshot85 | 14 Jan, 2023, 09:58: PM
Expert Answer
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  = begin mathsize 14px style 2 m space cross times space left parenthesis 2 l right parenthesis squared cross times fraction numerator w over denominator 2 l end fraction end style = ( 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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