Two equal uniform rods P and Q move with the same velocity v as shown in the figure. The second rod has an angular velocity `omega(lt 6v//l)` (clockwise) about G in addition to v.

Options

A. If the ends A and A' are suddenly fixed simultaneously both rods will rotate with the same angular velocity
B. If the ends A and A' are suddenly fixed simultaneously the rod Q will rotate with greater angular velocity
C. If the ends B and B' are suddenly fixed simultaneously both rods will rotate with the same angular velocity
D. If the ends B and B' are suddenly fixed simultaneously, the rod P will rotate with greater angular velocity

Answer

B, D

Explanation

The torque about the fixed point is zero, therefore angular momentum about this point will remain conserved when A and A' are fixed,
`L_(P)=mvl/2=(ml^(2))/3xxw_(F)`
`L_(Q)=mvl/2+(ml^(2))/3w=(ml^(2))/3xxw_(Q)`
`:.w_(Q) gt w_(P)`
When B and B are fixed
`L_(P)=(mvl)/2=(mvl)/3xxw_(P)`
`L_(Q)=(mvl)/2=(ml^(2))/3xxw_(Q)`
:.`w_(Q)ltw_(P)`