A ring of radius `R` having total charge `Q` uniformly distributed over the ring has a charge particle `q` kept at its centre. If a transverse pulse is created on the ring, then find the time when pulse completes one revolution.(Total mass of ring is `m`)

Options

A. `3piRsqrt((QqmR)/(piepsilon_(0)))`
B. `4piRsqrt((QqmR)/(piepsilon_(0)))`
C. `3piRsqrt((piepsilon_(0)mR)/(Qq))`
D. `4piRsqrt((piepsilon_(0)mR)/(Qq))`

Explanation

`2Tsin((d theta)/(2))=(1)/(4piepsilon_(0))((Q)/(2pi)d theta)q//R^(2)`
`T=(1)/(8pi^(2)epsilon_(0))(Qq)/(R^(2))`
Velocity of pulse
`v=sqrt((T)/(mu))=sqrt((1)/(8pi^(2)epsilon_(0))(Qq)/(R^(2))//(m)/(2piR))=sqrt((Qq)/(4piepsilon_(0)mR))`
`mu` is mass per unit length
Time `=(2piR)/(v)=2piRsqrt((4piepsilon_(0)mR)/(Qq))`