Correct Answer - A
Given that `I_(0)` is the moment of inertia of table and gun and m the mass of bullet.
Initial angular momentum of system about centre:
`L-i=(I_(0)+mr^(2))omega_(0)`……..i
Let `omega` be the angular velocity of the table affter the bullet is fired.
Final angular momentum
`L_(f)=I_(0)omega-m(v-romega)r`.........ii
Where `(v-romega)` is absolute velocity of bullet to the right.
Equating i and ii we get `(omega-omega_(0))=(mvr)/(I_(0)+mr^(2))`
This is also the increase in angular velocity.