Réitigh 3(9.81)=6.67(10^-11)(m/r^2)-(w^2)r

$$3 ( 9.81 ) = 6.67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

Réitigh do m.

$$m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}$$

$$r\neq 0$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi r^{2}.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}rr^{2}$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 1 agus 2 chun 3 a bhaint amach.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Méadaigh 3 agus 9.81 chun 29.43 a fháil.

$$29.43r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Ríomh cumhacht 10 de -11 agus faigh \frac{1}{100000000000}.

$$29.43r^{2}=6.67\times \frac{1}{100000000000}m-w^{2}r^{3}$$

Méadaigh 6.67 agus \frac{1}{100000000000} chun \frac{667}{10000000000000} a fháil.

$$29.43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}$$

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$\frac{667}{10000000000000}m-w^{2}r^{3}=29.43r^{2}$$

Cuir w^{2}r^{3} leis an dá thaobh.

$$\frac{667}{10000000000000}m=29.43r^{2}+w^{2}r^{3}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}$$

Roinn an dá thaobh den chothromóid faoi \frac{667}{10000000000000}, arb ionann é sin agus an dá thaobh a mhéadú faoi dheilín an chodáin.

$$\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Má roinntear é faoi \frac{667}{10000000000000} cuirtear an iolrúchán faoi \frac{667}{10000000000000} ar ceal.

$$m=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Roinn r^{2}\left(29.43+w^{2}r\right) faoi \frac{667}{10000000000000} trí r^{2}\left(29.43+w^{2}r\right) a mhéadú faoi dheilín \frac{667}{10000000000000}.

$$m=\frac{10000000000000r^{2}\left(rw^{2}+29.43\right)}{667}$$