An impulse J $$=$$ mv at one end of a stationary uniform frictionless rod of mass m and length l which is free to rotate in a $$gravity-free$$ space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through

Question

An impulse J $$=$$ mv at one end of a stationary uniform frictionless rod of mass m and length l which is free to rotate in a $$gravity-free$$ space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through

Infinity Learn · Accepted Answer

J $$=$$ mv $$=$$ mv'⇒ Velocity of the CM of rod $$=$$ vApplying impulse momentum equation about the CM of rodAbout instantaneous axis of rotation the rod is considered to have pure rotation.Let instantaneous axis of rotation be located at a distance x from the colliding end [Fig (b)]ω$$l2$$−vl−$$x=v+$$ω$$l2x$$      .......(i)Substituting$$ the value of w $$=$$ $$6V/l$$ in eq. $$(i), we get $$x=23l$$..

An impulse J = mv at one end of a stationary uniform frictionless rod of mass m and length l which is free to rotate in a gravity-free space. The impact is elastic. Instantaneous axis of rotation of the rod will pass through

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