A satellite of mass M revolving in a circular orbit of radius `r_(s)` around the earth of mass M has a total energy E. then, its angular momentum will be

Options

A. `sqrt("E")/(m_(s)r_(s)^(2))`
B. `("E")/(2m_(s)r_(s)^(2))`
C. `sqrt(2" E m"_(s)r_(s)^(2))`
D. `sqrt(2" E m"_(s)r_(s)`

Answer

C

Explanation

We know that,
`("GMm"_(s))/(r_(s)^(2))=(m_(s)v_(s)^(2))/(r_(s))`
`v_(s)=((GM)/(r_(s)))^(1//2)`
Angular momentum `=m_(s)v_(s)r_(s)=J`
`:.J=((GM)/(r_(s)))^(1//2)m_(s)r_(s)=(GMm_(s)^(2)r_(s))^(1//2)`
`because" "KE=(1)/(2)m_(s)v_(s)^(2)=(1)/(2)(m_(s)GM)/(r_(s))`
`PE=(-GMm_(s))/(2 r_(s))`
Total energy `E=-("GMm"_(s))/(2r_(s))`
`:." "J=(2" Em"_(s)r_(s)^(2))^(1//2)`