A single conservative force acts on a $$1$$ kg particle that moves along $$x-axis$$. The potential energy of the particle varies with x as U $$=$$ $$20+$$ $$(x$$ $$-$$ $$2)2$$ here U is in joules and x is in meters. When the particle is at x $$=$$ $$5$$ m, its kinetic energy is $$20$$ J. Then which of the following $$is/are$$ correct ?

Question

Infinity Learn · Accepted Answer

$$U=20+(x$$−$$2)2$$ (a)  At $$x=5$$,$$U=20+32=29J$$                $$KE$$$$=20J$$∴ Mechanical energy $$=U+$$$$KE$$$$=49J$$ (c) $$Umin=20J$$ ∴ $$KEmax=29J$$ (b) $$KEmin=0$$ ∴ $$Umax=49=20+xmax$$−$$22$$        ⇒xmax−$$22=29$$        ⇒$$xmax=2$$±$$29$$ (d) For equilibrium $$dUdx=0$$       ⇒ $$x=2$$

A single conservative force acts on a 1 kg particle that moves along x-axis. The potential energy of the particle varies with x as U = 20+ (x - 2)² here U is in joules and x is in meters. When the particle is at x = 5 m, its kinetic energy is 20 J. Then which of the following is/are correct ?

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A single conservative force acts on a 1 kg particle that moves along x-axis. The potential energy of the particle varies with x as U = 20+ (x - 2)2 here U is in joules and x is in meters. When the particle is at x = 5 m, its kinetic energy is 20 J. Then which of the following is/are correct ?

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Ready to Test Your Skills?

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A single conservative force acts on a 1 kg particle that moves along x-axis. The potential energy of the particle varies with x as U = 20+ (x - 2)² here U is in joules and x is in meters. When the particle is at x = 5 m, its kinetic energy is 20 J. Then which of the following is/are correct ?