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A particle free to move along x-axis is ...

A particle free to move along x-axis is acted upon by a force `F=-ax+bx^(2) whrte a and b are positive constants. `For ximplies0`, the correct variation of potential energy function U(x) is best represented by.

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C
`F =(dU)/(dx)` or `dU=-Fdx=(ax=bx^(2))dx`
Assuning `U=0` at `x=0`, and integrating the above equation we get,
`U = (ax^(2))/2-(bx^(3))/3`
`U-0` at `x=0` and `x=(3a)/(2b)`
For `xgt(3a)/(2b), bx^(3)/3gtax^(2)/2` and U will become negative. So, option (c) is the most approprite answer.
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