$A$ hemisphere of radius $R$ and mass $4m$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to the hemisphere at an angular displacement $\theta$ when the velocity of the hemisphere is $v$ is:

• A
  $\frac{5v}{R \cos \theta}$
• B
  $\frac{2v}{R \cos \theta}$
• C
  $\frac{3v}{R \sin \theta}$
• D
  $\frac{5v}{R \sin \theta}$