A particle of mass m is located in a potential field given by U (x) = `U_(o)` (1-cos ax) where `U_(o)` and a are constants and x is distance from origin. The period of small oscillations is

Options

A. `sqrt((U_(o))/(ma^(2)))`
B. `sqrt((mU_(o))/(a^(2)))`
C. `sqrt((a)/(mU_(o)))`
D. `sqrt((m)/(U_(o)a^(2)))`

Answer

D

Explanation

`U=U_(o)(1-cosax)`
`F=(dU)/(dx)`
`=-U_(o)("a sinax")`
`(because"For small oscillation becausesin` ax `~~` ax)
`=-aU_(o)(ax)`
effective `K=a^(2)U_(o)`
`T=2pisqrt((m)/(a^(2)U_(o)))`