A rod of mass $$0.720$$ kg and radius $$6$$ cm rests on two parallel rails that are $$d=12$$ cm apart and length of rails is $$L=49$$ cm. The rod carries a current of $$i=48$$ A in the direction shown in figure. And rolls along the rails without slipping. A uniform magnetic field of magnitude $$0.240$$ T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails.

Question

A rod of mass $$0.720$$ kg and radius $$6$$ cm rests on two parallel rails that are $$d=12$$ cm apart and length of rails is  $$L=49$$ cm. The rod carries a current of $$i=48$$ A in the direction shown in figure. And rolls along the rails without slipping. A uniform magnetic field of magnitude $$0.240$$ T is directed perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod as it leaves the rails.

Infinity Learn · Accepted Answer

Using work energy theorem,  Wby Magnetic force $$+Wby$$ $$friction=$$Δ$$KE$$ ⇒$$FL=12mv2+12Iw2$$   [Static friction does no work during pure rolling] ⇒Bid $$L=12mv2+1212mr2(vr)2$$ ∴ $$V=43idBLm=4$$×$$48$$×$$0.12$$×$$0.240$$×$$0.493$$×$$0.720=1.12m/s$$

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