Q.

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

Mechanical energy of particle is 49 J.

b

Least and greatest value of x between which particle can move is (2 - 29) m and (2+ 29) m respectively.

c

Maximum kinetic energy of the particle is 29 J.

d

At x = 2, the body is in equilibrium.

answer is A.

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Detailed Solution

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
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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 ?