The time period of an artificial satellite in a circular orbit of radius `R` is `2` days and its orbital velocity is `v_(0)`. If time period of another satellite in a circular orbit is `16` days then

Options

A. Its radius of orbit is `4R` and orbital velocity is `v_(0)`
B. Its radius of orbit is `4R` and orbital velocity is `(v_(0))/2`
C. Its radius of orbit is `2R` and orbital velocity is `n_(0)`
D. Its radius of orbit is `2R` and orbital velocity is `(v_(0))/2`

Answer

B

Explanation

According to Kepler's third law
`T^(2) prop R^(2)`
`:. (T_(1))/(T_(2))=((R_(1))/(R_(2)))^(3//2)`
or `R_(2)=(R_(1))((T_(1))/(T_(2)))^(2//3)=(R_(1))(16/2)^(2//3)`
`=4R_(1)=4R` (given `R_(1)=R)`........(i)
Orbital velocity, `v_(0)=sqrt((GM)/R)`
`:. (v_(02))/(v_(01))=sqrt((R_(1))/(R_(2)))=sqrt((R_(1))/(4R_(1)))=1/2` (using (i))
or `v_(02)=1/2v_(01)=1/2v_(0)`