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Given below is the plot of a potential e...

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose tha `E_("mech")=8` J, the incorrect statement for this system is :

A

At `x = x_(2)`, K.E. is greatest and the particle is moving at the fastest speed

B

At `x lt x_(1)`, K.E. is smallest and the particle is moving at the slowest speed

C

At `x =x_(3)`, K.E. = 4J

D

At `x gt x_(4)`, K.E. is constant throughout the region

Text Solution

Verified by Experts

The correct Answer is:
B
`E_("mech")= 8J`
In option (a), At `x= x_(2), U= 0 rArr E_("mech")= K= 8J`
KE is greatest, and particle is moving at fastest speed In option (b) At `x lt x_(1)`, U= constant= 8J
`K= E_("mech")- U= 8- 8= 0J`
`therefore` Particle is at rest
In option (c), At `x = x_(3), U= 4J`
`because U+ K= 8J`
`therefore K= 4J`
In option (d), At `x gt x_(4)`, U= constant = 6J
`K= E_("mech")- U= 2J`= constant
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