A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses 
and 
are moving in opposite directions with same speed of 
and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency 
. The ratio of 
and 
is :
Text Solution
Verified by ExpertsB
Linear momentum conservation: 
, giving 
.
Angular momentum about center of mass from the collision geometry:
Taking collision points 2 cm and 4 cm from the 12 cm bar's center at different positions, the angular momentum is
.
Calculating moment of inertia: 
The angular frequency 
is obtained from 
, giving ratio 
.
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