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The potential energy U=3ax^(3)-2bx^(2). ...

The potential energy `U=3ax^(3)-2bx^(2)`. The force constant is represented by

A

8b

B

6b

C

4b

D

2b.

Text Solution

Verified by Experts

The correct Answer is:
C
Given, potential energy `U=3ax^(3) - 2 bx^(2)`.
We know force constant, `k=(d^2 U)/(dx^2)`
`therefore (dU)/(dx)= 9ax^(2) - 4 bx`.
At equilibrium, `(dU)/(dx)=0`
`therefore 9ax^(2) - 4 bx =0` or `x=(4b)/(9a)`.
`therefore (d^2 U)/(dx^2)=18 ax-4b`. At `x=4b//9a`.
`k=(d^2 U)/(dx^2) = (18a xx 4b)/(9a) - 4b-=4b`.
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