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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)` |
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Answer» Correct Answer - 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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