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The potential energy of a particle of mass 1 kg is $U = 10 + (x - 2)^{2}$ . Here, U is in joule and x in metre on the positive X-axis. Particle can travel maximum upto x = + 6 m. Choose the correct option.

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On negative X-axis, particle travels upto x = $-$ 4 m

The maximum kinetic energy of the particle is 10 J

The maximum kinetic energy of the particle is 16 J

The minimum kinetic energy of the particle is 10 J

answer is C.

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Detailed Solution

At x = 6 m, U = 26J (extreme position)

On the other side, $U = 26 = 10 + (x - 2)^{2} or x - 2 = \pm 4$

$∴ x = 6 m and x = - 2 m$

$U_{\min} = 10 J, at x = 2 m$

${KE}_{\max} = E - U_{\min} = 16 J, at x = 2$

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