A particle of charge `-q` and mass `m` moves in a circular orbits of radius `r` about a fixed charge `+Q`.The relation between the radius of the orbit `r` and the time period `T` is

Options

A. `r = (Qq)/(16 pi ^(2) in_(0) m)T^(2)`
B. `r^(3) = (Qq)/( 16 pi^(3) in _(0) m)T^(2)`
C. `r^(2) = (Qq)/(16 pi^(3) in_(0) M)T^(3)`
D. `r^(2) = (Qq)/(4 pi^(3) in_(0) M)T^(3)`

Answer

B

Explanation

By Newton.s second law,
`(1)/(4 pi in_(0)) (Qq)/(r^(2)) = (mv^(2))/(r), or v = sqrt((Q q)/( 4 pi in_(0) m r))`
Now time period, ` T = (2 pi r)/( v) = (2 pi r)/(sqrt((Q q)/( 4 pi in_(0) mr)))`
or ` r^(3) = (( Q q)/(16 pi ^(3) in_(0) m)) T^(2)`