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Question

The potential energy of a particle of mass 1 kg is , U=10+(x2)2. Here U is in joule and x in metre on the positive x-axis. Particle travels upto x=+6 m. Choose the appropriate answer.

A
On negative x-axis particle travels upto x=2 m
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B
The maximum kinetic energy of the particle is 16 J
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C
Both (a) and (b) are correct
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D
Both (a) and (b) are wrong
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Solution

The correct option is C Both (a) and (b) are correct
At x=6 m,U=26 J
On the other side
U=26=10+(x2)2
or x2=±4
x=6 m
and x=2 m
Thus x=+6 m and x=2 m are the extreme positions. At x=2 m , potential energy is minimum, which is 10 J. Hence, at this position kinetic energy will be maximum, which is equal to total mechanical energy (=26 J) minus minimum potential energy (=10 J). Thus maximum kinetic energy is 16 J

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