A large rectangular box has been rotated with a constant angular velocity `omega_(1)` about its axis as shown in the figure. Another small box kept inside the bigger box is rotated in the same sense with angular velocity `omega_(2)` about its axis (which is fixed to floor of bigger box). A particle `P` has been identified, its angular velocity about `AB` would be

Options

A. `(omega_(2)(r_(2)-r_(1))+omega_(1)r_(2))/(r_(2))`
B. `(omega_(2)(r_(2)-r_(1))+omega_(1)r_(1))/(r_(2))`
C. `omega_(1)`
D. `omega_(2)`

Answer

B

Explanation

`vec(V),CD=omega_(2)(r_(2)-r_(1)),vec(V),CD,AB=omega_(1)r_(1)`
`vec(V)_(P),AB=vec(V)_(P),CD+vec(V)_(CD),AB`
`=omega_(2)(r_(2)-r)+omega_(1)r_(1)`
Angular velocity of `P` about `AB`
`omega=(v_(PAB))/(r_(2))=omega_(2)(r_(2)-r_(1))+omega_(1)(r_(1))/(r_(2))`