A particle located in one dimensional potential field has potential energy function`U(x)=(a)/(x^(2))-(b)/(x^(3))`, where a and b are positive constants. The position of equilibrium corresponds to x equal to

Options

A. `(3a)/(2b)`
B. `(2b)/(3a)`
C. `(2a)/(3b)`
D. `(3b)/(2a)`

Answer

`(4)`

Explanation

`F = - (dU)/(dx) = 0`
`(2a)/x^(3) + (3b)/(x^(4)) = 0`
` -2ax + 3b = 0 Rightarrow x = (3b)/(2a)`