A plank P is moving with constant velocity V on a horizontal surface. A disc of radius R is rolling without slipping on the plank with a velocity V relative to the plank. Then radius of curvature of the trajectory of a point on the circumference of the ring when it is at position A, as viewed by an observer standing on the ground is

Question

Infinity Learn · Accepted Answer

As viewed by an observer on the ground, velocity of A is given byV→A $$=V$$→C $$+$$ V→$$A/C$$ $$=$$ $$V+V$$ $$i^+$$ω$$Rj^$$ $$=2vi^+vj^$$∴         VA $$=$$  $$2v2$$ $$+v2$$ $$=$$ $$5$$ VNow acceleration of A is given bya→A $$=$$ a→C $$+$$ a→$$A/C$$ $$=$$  $$0$$  $$+$$  ω$$2Ri$$  $$=$$  $$v2R$$  $$i^$$∴     $$VA2$$ρ $$=$$  aA ⇒  $$5$$ $$v2$$ρ  $$=$$  $$v2R$$  ⇒  ρ $$=$$  $$5R$$

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