InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A body of mass m is situated in a potential field `U(x)=U_(0)(1-cosalphax)` when `U_(0)` and `alpha` are constant. Find the time period of small oscialltions.A. `2pisqrt((m)/(U_(0)alpha))`B. `2pisqrt((m)/(U_(0)alpha^(2)))`C. `2pisqrt((m)/(2U_(0)alpha))`D. `2pisqrt((2m)/(U_(0)alpha^(2)))` |
|
Answer» Correct Answer - B Given: `U=U_(0)(1-cosalphax)` `becauseF=-(dU)/(dx)` `thereforeF=-(d)/(dx)[U_(0)(1-cosalphax)]=-U_(0)alphasinalphax` As `alphax` is small, so `sinalphax ~ alphax` `thereforeF=-U_(0)alpha^(2)x` . .. (i) `Fpropx and -ve` shows that F is directed towards the mean position, hence the body executes SHM. For SHM, `F=-kx` Comparing (i) and (ii), we get, `k=U_(0)alpha^(2)` Time period of oscillation, `T=2pisqrt((m)/(k))=2pisqrt((m)/(U_(0)alpha^(2)))` |
|