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Question: A body of mass m is situated in a potential field U(x) = U0(1 – cos\(\alpha\)x) where U0 and a are c...

A body of mass m is situated in a potential field U(x) = U0(1 – cosα\alphax) where U0 and a are constants the time period of small oscillations is.

A

B

C

2π m2U0α2 \pi \sqrt { \frac { \mathrm {~m} } { 2 \mathrm { U } _ { 0 } \alpha } }

D

Answer

Explanation

Solution

Given

∵F=−dUdx\because \mathrm { F } = - \frac { \mathrm { dU } } { \mathrm { dx } }

As αx\alpha x is small so

…… (i)

and –ve shows that F is directed towards the mean position hence the body execute SHM.

For SHM, F =-kx ….. (ii)

Comparing (i) and (ii) we get

Time period of oscillation,