A body of mass m is situated in a potential field `U(x)=U_(0)(1-cosalphax)` where `U_(0) and alpha` are constants. The time period of small oscillations i

Options

A. `2pisqrt((m)/(aU_(0)))`
B. `2pisqrt((am)/(U_(0)))`
C. `2pisqrt((m)/(a^(2)U_(0)))`
D. `2pisqrt((3^(2)m)/(U_(0)))`

Answer

C

Explanation

Restoring Force `F = (-du)/(dx) = (-d)/(dx) (u_(0) (1-cos ax)`
`F(x) = -u_(0)asinax`
for small angle `sin ax approx ax`
`F = -u_(0)a^(2)x rArr acc. (-u_(0)a^(2)x)/(m) = -omega^(2)x = ((2pi)/(T))^(2) xx x`
So, Time speed period `T = 2pisqrt((m)/(u_(0)a^(2)))`