The satellite of mass m revolving in a circular orbit of radius r around the earth has kinetic energy E. then, its angular momentum will be

Options

A. `sqrt(E )/(mr^(2))`
B. `(E )/(2mr^(2))`
C. `sqrt(2 Emr^(2))`
D. `sqrt(2 Emr)`

Answer

C

Explanation

If m is the mass and v is the orbital velocity of the satellite then its kinetic energy
`E=1/2 mv^(2) rarr Em =1/2 m^(2)v^(2)`
or `m^(2)v^(2)=2Em`
`rarr mv=sqrt(2Em)`
if r is the radius of the orbit of the satellite then its angular momentum L= mvr
using Eq i we get `L=sqrt(2Em) r=sqrt(2Emr^(2))`