Question Number 29144 by tawa tawa last updated on 04/Feb/18
$$\mathrm{A}\:\mathrm{body}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{orbit}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{4R}\:\mathrm{round}\:\mathrm{the}\:\mathrm{earth}.\:\:\mathrm{Express}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{free}\:\mathrm{fall}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{g} \\ $$$$\mathrm{R}\:=\:\mathrm{radius}\:\mathrm{if}\:\mathrm{the}\:\mathrm{earth} \\ $$$$\mathrm{g}\:=\:\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity} \\ $$
Answered by ajfour last updated on 04/Feb/18
$$\frac{{GMm}}{\left(\mathrm{4}{R}\right)^{\mathrm{2}} }=\:{ma} \\ $$$$\Rightarrow\:\:\:{a}\:=\frac{{GM}}{\mathrm{16}{R}^{\mathrm{2}} }\:=\:\frac{{g}}{\mathrm{16}}\:. \\ $$
Commented by tawa tawa last updated on 04/Feb/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by tawa tawa last updated on 04/Feb/18
$$\mathrm{Please}\:\mathrm{how}\:\mathrm{did}\:\mathrm{it}\:\mathrm{becomes}\:\:\:\frac{\mathrm{g}}{\mathrm{16}}\:\:\mathrm{from}\:\:\:\:\frac{\mathrm{GM}}{\mathrm{16R}^{\mathrm{2}} } \\ $$
Commented by tawa tawa last updated on 04/Feb/18
$$\mathrm{or}\:\:\:\:\:\mathrm{g}\:=\:\frac{\mathrm{GM}}{\mathrm{R}^{\mathrm{2}} } \\ $$
Commented by ajfour last updated on 04/Feb/18
$${yes}. \\ $$
Commented by tawa tawa last updated on 04/Feb/18
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you} \\ $$