InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
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). For periodic motion of small amplitude A,the time period (T) of thes particle is proportional to.A. `Asqrt((m)/(alpha))`B. `(1)/(A)sqrt((m)/(alpha))`C. `Asqrt((alpha)/(m))`D. `(1)/(A)sqrt((alpha)/(m))` |
|
Answer» Correct Answer - B `V = alphaX^(4)` `T.E. = (1)/(2) momega^(2)A^(2) = alphaA^(4)` (not stricltly applicable just for dimension matching it is used) `omega^(2) = (2alphaA^(2))/(m) rArr T prop (1)/(A)sqrt((m)/(alpha))` |
|