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6. A uniform solid cone of mass m, base radius 'R' and height 2R, has a smooth groove along itsslant height as shown in figure. The cone is rotating with angular speed 'o', about the axis ofsymmetry. If a particle of mass 'm' is released from apex of cone, to slide along the groove, thenangular speed of cone when particle reaches to the base of cone is2 RR30(A)13500(C)1340(B)1390(D)13 |
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Answer» oment of inertia of cone about the AXIS shown in figure is = 3/10mR squareHere, R= radius of conem= mass of coneWhen the particle is at apex it has no moment of inertia about axis of rotation .When the particle is at the base of cone it has a moment of inertia which is equal to m/s SQUARE.So, INITIALLY the moment of inertia of system is II = 3/10mR square+0= 3/10mR squareFinally the moment of inertia of the system I f =3/10mR square+mR square =13/10mR squareSo according to CONSERVATION of angular momentum I iw=I fw'⟹ω'= I'i/ If w ω'=(3/10)mR square/(13/10)mR square⟹ω =3w'/13 |
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