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Question Number 24712 by ajfour last updated on 25/Nov/17

Commented by ajfour last updated on 25/Nov/17

$O r i g i n a l l y a p l a n e t o f r a d i u s R,$ $o f u n i f o r m d e n s i t y, h a s a g r a v i t a t i o n a l$ $f i e l d a t i t s s u r f a c e e q u a l t o g .$ $B e c a u s e a s p h e r e o f c r u s t o f$ $r a d i u s r i s r e m o v e d g r a v i t a t i o n a l$ $f i e l d e x p e r i e n c e d b y t h e f i g u r e$ $a t t h e s u r f a c e r e d u c e s t o g / 2 .$ $F i n d r / R .$
Commented by mrW1 last updated on 25/Nov/17

$g = \frac{G M}{R^{2}}$ $\frac{g}{2} = \frac{G m}{r^{2}}$ $2 = \frac{{M r}^{2}}{{m R}^{2}} = {(\frac{R}{r})}^{3} \frac{r^{2}}{R^{2}} = \frac{R}{r}$ $\Rightarrow \frac{r}{R} = \frac{1}{2}$
Commented by ajfour last updated on 25/Nov/17

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