Question

derive mathematical expression to find the weight of an object on moon in comparison with that on earth​

Answer 1

$\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 $\frac{M_m\:×\:m}{R_m²}$ ${\longrightarrow}$ $( 1 )$

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}}$ = $\bold{\frac{1}{6}}$

$\therefore$ $\sf{Weight\: of\:obj.\:in\:moon}$ = $\frac{1}{6}$ × $\sf{its\: weight\: on\: earth}$

$\boxed{\boxed{\boxed{\bf{PROVED}}}}$ $\blacksquare{\tiny{BY}}\blacksquare$ $\boxed{\boxed{\boxed{\mathbb{@\:LILY}}}}$

Answer 2

$\huge\frak\pink{answer}$

gravity

Explanation:

gravity is 900 psi power of weight