A uniform rod of mass M and length L is hinged at lower end on a fixed horizontal table. The rod can rotate freely in vertical plane and there is no friction at the hinge. A ball of mass M and radius $$R=L3$$ is placed in contact with the vertical rod and a horizontal force F is applied at the upper end of the rod. There is no friction between rod and the ball and there is sufficient friction between ball and ground for pure rolling. Mark the correct $$statement(s)$$. (assume$$ the ball to be a uniform solid $$sphere)

Question

A uniform rod of mass M and length L is hinged at lower end on a fixed horizontal table. The rod can rotate freely in vertical plane and there is no friction at the hinge. A ball of mass M and radius $$R=L3$$ is placed in contact with the vertical rod and a horizontal force F is applied at the upper end of the rod. There is no friction between rod and the ball and there is sufficient friction between ball and ground for pure rolling. Mark the correct $$statement(s)$$. (assume$$ the  ball to be a uniform solid $$sphere)

Infinity Learn · Accepted Answer

For ball: N⋅$$R=25+1MR2a0R$$⇒$$N=75Ma0$$      .....(i)     For rod : F−$$N3l=Ml23$$α   .....(ii)  Also, lα$$3=a0$$  (iii) From (i), (ii) & (iii) $$a0=1522$$  FM  ;  α$$=3a0l=45$$ $$F22$$  $$Mlb)$$ Horizontal hinge reaction  Rx is horizontal Hinge reaction and Ry is vertical Hinge $$reactionF+Rx-N=MacomRx=-F+N+Macom=$$ $$-F+75Ma0+M$$α$$l2=-F+75M15F22M+M45F22Mll2$$ $$=43F44$$

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