Question

why is the weight of an object on the moon 1/6th its weight on the earth

Answer 1

because of the acceleration due to gravity on the moon is 1/6 time of acceleration due to gravity on the earth
thats why gravitational Force also 1/6 time on the earth
and as we know
weight of an object is the force due to gravity so weight is also 1/6 times

Answer 2

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

Weight = mass × acceleration due to gravity

( W = mg)

Value of g on earth , ge = 9.8 m${s}^{-2}$

Value of g on moon, gm = 1.6 m${s}^{-2}$

$\frac{gm}{ge}$ = $\frac{1.6}{9.8}$ = $\frac{1}{6}$

$\frac{Weight\:on\:moon}{Weight\:on\:earth}$ = $\frac{mgm}{mge}$ = $\frac{1}{6}$

Weight on moon = $\frac{1}{6}$ (Weight on earth).