When a particle of mass m moves on the x-axis in a potential of the form `V(x) =kx^(2)` it performs simple harmonic motion. The correspondubing time period is proprtional to `sqrtm/h`, as can be seen easily using dimensional analusis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of `x=0` in a way different from `kx^(2)` and its total energy is such that the particle does not escape toin finity. Consider a particle of mass m moving on the x-axis. Its potential energy is `V(x)=ax^(4)(agt0)` for |x| neat the origin and becomes a constant equal to `V_(0)` for `|x|impliesX_(0)` (see figure).
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The acceleration of this partile for `|x|gtX_(0)` is
(a) proprtional to `V_(0)`
(b) proportional to.

Options

A. (a) proprtional to `V_(0)`
B. (b) proportional to `V_(0)/(mX_(0))
C. (c ) proportional to `sqrtV_(0)/(mX_(0)`
D. (d) zero`.

Answer

D

Explanation

(d) `F=(-dV(x))/(dx)`
As `V(x)=constamt for `xgtX_(0)`
Since `F=0,a=0`.