Question

Prove that I'm =1/6 × We or weight of the object on moon = 1/6 × weight of the object on Earth?​

Answer 1

Answer:

The mass of moon is 1/100 times and its radius 1/4 times that of earth. As a result, the gravitational attraction on the moon is about one sixth when compared to earth. Hence, the weight of an object on the moon is 1/6th its weight on the Earth.

Answer 2

Explanation:

$we = g \times \frac{mem}{r {m}^{2} }$

$weight \: of \: the \: object \: on \: the \: moon \: is$

$wm = g \times \frac{ {m}^{2 - m} }{r {m}^{2} }$

$so \: the \: ratio \: of \: the \: object \: of \: the \:$

$moon \: to \: weight \: on \: earth \: is$

$\frac{wm}{we} = \frac{gmm - m}{r {m}^{2} } \times \frac{r {e}^{2} }{gmem}$

$\frac{wm}{we} = \frac{mm}{me} \times ( \frac{re}{rm} ) {}^{2}$

$\frac{mm}{100mm} \times ( \frac{4rm}{rm} ) {}^{2}$

$\frac{16}{100} = \frac{1}{6}$

$therefore \: the \: weight \: of \: an \: object \:$

$on \: the \: moon \:is \: \frac{1}{6} of \: its\: weight \: on \: the \: earth$

$thanks$