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A folded plate OABCDEFO made of material...

A folded plate `OABCDEFO` made of materials such that part `OABO` (say part(i), `BCDOB` hs mass `4m, m` and `m` respectively. Part (i) is a uniform semicircular plate of radius `R//2` and in on the `xy` plane. Part (ii) and (iii) each is a uniform quarter circular plate of radius `R` on `xy` and `xz` plane respectively. The whole system is free to rotate about `y`-axis A particle `P` of mass `m` moving with velocity `v_(0)` hits to a point located at the circumcentre of the part (iii) and sticks to it. The point is at a distance `R//2` from `x` -axis as shown in the figure. Angular velocity of the combined system just after the collision is

A

`(v_(0))/(4R)`

B

`(2v_(0))/(5R)`

C

`(3v_(0))/(5R)`

D

`(v_(0))/(2R)`

Text Solution

Verified by Experts

The correct Answer is:
A
Moment of inertia of combined system about `y` -axis
`=(4m(R/2)^(2))/4+(mR^(2))/4+(mR^(2))/2+mR^(2)=2mR^(2)`
Conservation of angular momentum along `y`-axis
`mv_(0) R/2=2mR^(2)omega`
`omega=(v_(0))/(4R)`
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