A communication satellite of mass `500kg` revolves around the earth in a circular orbit of radius `4.0xx10^(7)m` in the equatorial plane of the earth in the direction from west to east. The magnitude of angular momentum of the satellite is

Options

A. `~1.3xx10^(14)m^(2)s^(-1)`
B. `~0.58xx10^(14)m^(2)s^(-1)`
C. `~2.58xx10^(14)m^(2)s^(-1)`
D. `~0.13xx10^(14)m^(2)s^(-1)`

Answer

B

Explanation

As the satellite is revolving around earth in equatorial plane with orbital radius `4xx10^(7)m`,
Hence, the satellites is geostationary satellite.
The time period `T=24h=86400s`
Velocity of satellites, `V=(2pir)/R`
Angular momentum, `L=mvr`
`L=h((2pir)/R)r=(2pim)/R r^(2)`
`L=(2xx3.14xx500)/86400xx(4xx10^(7))^(2)`
`=0.58xx10^(14)kgm^(2)s^(-1)` (approx).