A rigid horizontal smooth rod AB of mass 0.75 kg and length 40 cm can rotate freely about a fixed vertical axis through its mid-point O. Two rings each of mass 1 kg initially at rest at a distance 10 cm from O on either side of the rod. The rod is rotated with angular velocity of 30 rad `s^(-1)`. When the rings reach the ends of the rod, the angular velocity of the rod is :

Options

A. 5
B. 10
C. 15
D. 20

Answer

B

Explanation

In this case `I_(1)omega_(1)=I_(2)omega_(2)`
or `((ML^(2))/(12)+2mr^(2))omega_(1)=((ML^(2))/(12)+2m(L^(2))/(4))omega_(2)`
Putting the values
`=[(0.75xx(0.4)^(2))/(12)+2xx1xx(0.1)^(2)]2pixx30`
`=[(0.75xx(0.4)^(2))/(12)+2xx(0.2)^(2)]xx2pin_(2)`
`n_(2)=((0.01+0.02)30)/((0.01+0.08))=(30xx0.03)/((.09))=10r.p.s.`