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

Question

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

Tardigrade Admin · Accepted Answer

L=m v r=m √(G M/r) r=m √G M r ∴ L propto √r ⇒ (L2/L1) =√(r2/r1) =√(16 r/r)=4 ⇒ L2=4 L

Q. 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

$16 L$

$64 L$

$\frac{L}{4}$

$4 L$

$L = m v r = m \frac{GM}{r} r = m GM r$
$∴ L \propto r$
$\Rightarrow \frac{L _{2}}{L _{1}} = \frac{r _{2}}{r _{1}}$
$= \frac{16 r}{r} = 4$
$\Rightarrow L_{2} = 4 L$

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

16L

64L

4L​

4L