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A particle of mass m is located in a one...

A particle of mass m is located in a one dimensional potential field where potential energy is given by V(x) = A(1 - cospx), where A and p are constants. The period of small oscillations of the particle is

A

`2pi sqrt(m/(Ap))`

B

`2pi sqrt(m/(Ap^(2)))`

C

`2pi sqrt(m/A)`

D

`1/(2pi) sqrt((Ap)/m)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `V(x) =A(1-cos px)`
Force, `F =-(dV)/(dt) =-d/(dx) (A-A cos px) =-Ap sinpx`
For small x, `F =-Ap^(2)x`
Acceleration, `a=F/m =-(Ap^(2)x)/m`.............(i)
The standard equation of SHM is,
`a=-omega^(2)x`...........(ii)
Comparing (i) and (ii), we get
`omega^(2) =(Ap^(2))/m` or `omega =sqrt((Ap^(2))/m)`
Periodic of oscillation, `T =(2pi)/omega =2pisqrt(m/(Ap^(2))`
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