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 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)`

A large rectangular box has been rotated with a constant angular veloc

1.	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 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» Correct Answer - B `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))`

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