The orbital angular momentum of a satellite revolving at a distance r from the centre is L . If the distance is increased to 16 r, then the new angular momentum will be

Options

A. `16 L`
B. `64 L`
C. `(L)/(4)`
D. `4 L`

Answer

D

Explanation

`L=mvr=msqrt((GM)/(r))r=m sqrt(GMr)`
`:. L prop sqrt(r)`
`rArr (t_(1))/(t_(2))=sqrt((r_(2))/r_(2))rArr (L)/(L_(2))=sqrt((r_(1))/(r_(2)))" "{(because L_(1)= "L,"),(" "r_(1)=r),(" "r_(2)=16 r):}}`
`rArr (L)/(L_(2))=sqrt((r)/(16r))rArr(L)/(L_(2))=(1)/(4)rArrL_(2)=4L`.