derive mathematical expression to find the weight of an object on moon

1.	derive mathematical expression to find the weight of an object on moon in comparison with that on earth
Answer» $\red{❣︎}$ $\huge{\mathtt{\blue{\underline{\underline{ANSWER}}}}}$ $\red{❣︎}$ We Know That , $\implies$ g = $\frac{GM}{R²}$ also , W = mg $\implies$ W = $\frac{GMm}{R²}$ Let , MASS of the object be m Its WEIGHT on moon be $W_m$ $\bf{Let \:the\: mass \:of \:Moon }$ = $M_m$ $\bf{And\: the \:Radius \:of \:moon}$ = $R_m$ Applying UNIVERSAL Law of Gravitation , weight of the obj. in moon will be $\longrightarrow$ $\implies {W_m}$ = G $\frac{M_m\:×\:m}{R_m²}$ ${\longrightarrow}$ $( <klux>1</klux> )$ Let the weight of the same obj. on earth be $W_e$ $\bf{Mass \:of \:earth \:is \:M}$ $\bf{Radius \:of \:earth\: is \:R}$ $\implies {W_e}$ = G $\frac{M\:×\:m}{R²}$ ${\longrightarrow}$ $( 2 )$ $\therefore$ ( 1 ) , ( 2 ) $\implies W_m$ = G $\frac{7.36\:×\:10²²\:kg\:×\:m}{( 1.76\:×\:10⁶\:m)²}$ $\implies W_m$ = $\bf{2.431 × 10¹⁰\: G × m}$ $\longrightarrow ( 3 )$ and $\implies W_e$ = $\bf{1.474 × 10¹¹\:G × m}$ $\longrightarrow ( 4 )$ $now ,$ $\huge{\frac{3}{4}}$ $\implies$ $\bold{\frac{W_m}{W_e}}$ = $\bold{\frac{2.431\:×\:10¹⁰}{1.474\:×\:10¹¹}}$ = 0.165 = $\bold{\frac{1}{6}}$ $\implies$ $\bold{\frac{Weight\:of\:obj\:in\:moon}{weight\:of\:obj\:in\:earth}}$ = $\bold{\frac{1}{6}}$ $\therefore$ $\sf{Weight\: of\:obj.\:in\:moon}$ = $\frac{1}{6}$ × $\sf{its\: weight\: on\: earth}$ $\boxed{\boxed{\boxed{\bf{PROVED}}}}$ $\blacksquare{\tiny{BY}}\blacksquare$ $\boxed{\boxed{\boxed{\mathbb{@\:LILY}}}}$